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Dr. Mariusz Urbanski

Professor

University of North Texas

Department of Mathematics

(940) 565-3323

Email: urbanski@unt.edu

Education

  • Habilitation, Mathematical Institute of the Polish Academy of Sciences, 1991
    Major: Habilitation, Mathematics
    Specialization: Dynamical Systems
    Dissertation: N/A
  • PhD, Nicolaus Copernicus University, 1985
    Major: Mathematics
    Specialization: Dynamical Systems
    Dissertation: Invariant sets in smooth dynamical systems

Professional Positions

  • Professor, University of North Texas. University of North Texas. (1999 - Present).
  • Associate Professor, University of North Texas. University of North Texas. (1994 - 1999).
  • Assistant Professor, University of North Texas. University of North Texas. (1992 - 1994).
  • Assistant Visiting Professor, University of North Texas. University of North Texas. (1991 - 1992).
  • Research Professor, SFB 170, Goettingen (W. Germany). SFB 170, Goettingen (W. Germany). (1989 - 1991).
  • Research Professor, A. von Humboldt Found., Bonn (W. Germany). A. von Humboldt Found., Bonn (W. Germany). (1988 - 1989).
  • Professional

  • Assistant Professor, N. Copernicus University, Torun (Poland). N. Copernicus University, Torun (Poland). (1982 - 1992).

Professional Memberships

  • American Mathematical Society. (Present).

Teaching

Teaching Experience

    University of North Texas

  • MATH 1100 - College Algebra, 1 course.
  • MATH 1720 - Calculus II, 1 course.
  • MATH 2510 - Real Analysis I, 2 courses.
  • MATH 2520 - Real Analysis II, 1 course.
  • MATH 2700 - Linear Algebra and Vector Geometry, 3 courses.
  • MATH 3000 - Real Analysis I, 2 courses.
  • MATH 3410 - Differential Equations I, 3 courses.
  • MATH 3610 - Real Analysis II, 2 courses.
  • MATH 3740 - Vector Calculus, 2 courses.
  • MATH 4500 - Introduction to Topology, 2 courses.
  • MATH 4900 - Special Problems, 1 course.
  • MATH 5200 - Topics in Dynamical Systems, 1 course.
  • MATH 5310 - Real Analysis, 4 courses.
  • MATH 5450 - Calculus on Manifolds, 1 course.
  • MATH 5600 - Introduction to Topology, 2 courses.
  • MATH 5610 - Topology., 3 courses.
  • MATH 5620 - Topology, 7 courses.
  • MATH 5900 - Special Problems, 13 courses.
  • MATH 5910 - Special Problems, 2 courses.
  • MATH 5950 - Master's Thesis, 1 course.
  • MATH 6110 - Topics in Analysis, 4 courses.
  • MATH 6150 - Functional Analysis, 1 course.
  • MATH 6200 - Topics in Ergodic Theory, 13 courses.
  • MATH 6210 - Dynamical Systems Seminar, 2 courses.
  • MATH 6220 - Logic and Dynamics Seminar, 2 courses.
  • MATH 6610 - Topics in Topology and Geometry, 1 course.
  • MATH 6900 - Special Problems, 30 courses.
  • MATH 6910 - Special Problems, 4 courses.
  • MATH 6940 - Individual Research, 1 course.
  • MATH 6950 - Doctoral Dissertation, 40 courses.

Directed Student Learning

  • Doctoral Advisory Committee Chair, "Multifrctal Spectrum of Birkhoff's Averages," Mathematics. (2023).
  • Doctoral Advisory Committee Chair, "Transfinite topological dimension and transfinite Hausdorff dimension," Mathematics. (September 2019 - 2022).
  • Doctoral Advisory Committee Chair, "Orbit Counting in Dynamical Systems," Mathematics. (February 2018 - 2022).
  • Doctoral Advisory Committee Chair, "Continuity of Hausdorff dimension for cubic polynomials," Mathematics. (2016 - 2022).
  • Directed Individual/Independent Study, Mathematics. (January 2019 - December 2019).
  • Directed Individual/Independent Study, Mathematics. (January 2019 - December 2019).
  • Doctoral Advisory Committee Chair, "Non-Autonomous Dynamical Systems," Mathematics. (2016 - June 2018).
  • Doctoral Advisory Committee Chair, "Shrining targets in conformal non-autonomous IFSs," Mathematics. (2016 - June 2018).
  • Other (Disseertation Research Hours), Mathematics. (January 2017 - May 2018).
  • Dissertation Committee Member, "Available online," Mathematics. (January 1993 - 2017).
  • Doctoral Advisory Committee Chair, "Numerical Values of the Hausdorff and Packing Measures for Limit Sets of Iterated Function Systems," Mathematics. (2015 - August 2017).
  • Directed Individual/Independent Study, Mathematics. (January 2017 - May 2017).
  • Major Professor, "Random Iteration of Rational Functions," Mathematics. (2012 - 2012).
  • Major Professor, "Real Analyticity of Hausdorff Dimension of Disconnected Julia Sets of Cubic Parabolic Polynomials," Mathematics. (2012 - August 2012).
  • Major Professor, "Kleinian Groups in Hilbert Spaces," Mathematics. (2012 - 2012).
  • Major Professor, "GIBBS/EQUILIBRIUM MEASURES FOR UNBOUNDED LOCAL ENERGY FUNCTIONS ON \N^{Z^d}," Mathematics. (2011 - 2011).
  • Major Professor, "The Global Structure of Iterated Function Systems," Mathematics. (2009 - 2009).
  • Major Professor, "The Geometry of Baire Spaces," Mathematics. (2007 - 2007).
  • Major Professor, "Dynamics, Thermodynamic formalism and Perturbations of Transcendental Entire Functions of Finite Singular Type," Mathematics. (2005 - May 2005).
  • Major Professor, Mathematics. (2004 - 2004).
  • Major Professor, "Examples and Applications of Infinite Iterated Function Systems," Mathematics. (2000 - August 2000).
  • Major Professor, "Multifractal Analysis of Parabolic Rational Maps," Mathematics. (1998 - August 1998).

Awards and Honors

  • Faculty Research Award, Department of Mathematics, UNT. (2017).
  • Faculty Teaching Award, Department of Mathematics, UNT. (2013).
  • Faculty Research Award, Department of Mathematics, UNT. (2012).
  • Sierpinski Medal, Polish Mathematical Society & University of Warsaw. (2023).
  • Faculty Research Award, Department of Mathematics, UNT. (2021).
  • Scholarly Development Award, (1996).

Research

Published Intellectual Contributions

    Abstracts and Proceedings

  • with F. Gonzales and O. Jenkinson. (2003). On transfer operator of continued fractions with restricted entries.
  • with D. Mauldin. (1996). Dimensions and measures in innite iterated function systems.
  • Book

  • Urbanski, M., Monday, S., Roy, M. (2023). Non--Invertible Dynamical Systems, Volume 3: Analytic Endomorphisms of the Riemann Sphere. 69/3 430. De Gruyter; De Gruyter Expositions in Mathematics.
  • Urbanski, M., Kotus, J. (2023). Meromorphic Dynamics, Volume 1: Abstract Ergodic Theory, Geometry, Graph Directed Markov Systems, and Conformal Measures Meromorphic Dynamics, Volume 1: Abstract Ergodic Theory, Geometry, Graph Directed Markov Systems, and Conformal Measures. 46 (46) 490. Cambridge University Press; New Mathematical Monographs. https://www.cambridge.org/core/books/meromorphic-dynamics/D03DC52181507C71235ADB44891E1EE6
  • Urbanski, M., Kotus, J. (2023). Meromorphic Dynamics, Volume 2: Elliptic Functions with an Introduction to the Dynamics of Meromorphic Functions. 47 (47) 530. Cambridge University Press; New Mathematical Monographs [80% of original research]. https://www.cambridge.org/core/books/meromorphic-dynamics/D03DC52181507C71235ADB44891E1EE6
  • Urbanski, M., Monday, S., Roy, M. (2022). Non--Invertible Dynamical Systems, Volume 2: Finer Thermodynamic Formalism--Distance Expanding Maps and Countable State Subshifts of Finite Type, Conformal GDMSs, Lasota--Yorke Maps, and Fractal Geometry,. 69/2 510. De Gruyter; De Gruyter Expositions in Mathematics.
  • Urbanski, M., Munday, S., Roy, M. (2021). Non--Invertible Dynamical Systems, Volume 1: Ergodic Theory - Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps. 458. De Gruyter; De Gruyter Expositions in Mathematics.
  • Urbanski, M., Das, T., Simmons, D. (2017). Geometry and Dynamics in Gromov Hyperbolic Metric Spaces, with an Emphasis on Non-Proper Settings. 281. AMS Mathematical Surveys and Monographs Series.
  • (with F. Przytycki. (2010). Conformal Fractals: Ergodic Theory Methods. Cambridge University Press; The London Mathematical Society.
  • with D. Mauldin. (2003). Graph Directed Markov Systems: Geometry and Dynamics ofLimit Sets.
  • Conference Proceeding

  • Urbanski, M., Mayer, V. (2021). Thermodynamic Formalism and Geometric Applications for Transcendental Meromorphic and Entire Functions. 99-139. ``Thermodynamic Formaism”, Springer Lecture Notes in Mathematics, CIRM Jean Morlet Chair subseries.
  • Urbanski, M. (2014). Countable Alphabet Non-Autonomous Self-Affine Sets. 92 129-145. "Fractals, Wavelets, and their Applications", Springer Proceedings in Mathematics \& Statistics.
  • Urbanski, M., Mihailescu, E. (2013). Hausdorff Dimension of the Limit Set of Countable Conformal Iterated Function Systems with Overlaps. 600 273-290. Contemporary Mathematics.
  • Urbanski, M., Skorulski, B. (2013). The Law of Iterated Logarithm and Equilibrium Measures Versus Hausdorff Measures for Dynamically semi-Regular Meromorphic Functions. 213--234. Proc. Conf. "Further Developments in Fractals and Related Fields", in "Trends in Mathematics" of Birkhauser.
  • with A. Volberg. (1995). A rigidity theorem in complex dynamics, in Fractal Geometry andStochastics. Progress in Probability 37, Birkhauser Verlag (1995).
  • with M. Denker. (1992). The dichotomy of Hausdor measures and equilibrium statesfor parabolic rational maps. Springer's Lecture Notes in Mathematics.
  • Editorial Material

  • Urbanski, M. (2012). Special issue on Dynamical Systems II, Denton 2009; Conference Proceedings PREFACE. Discrete and Continuous Dynamical Systems. 32 (7) I-III.
  • Clark, A., Urbanski, M. (2005). Proceedings of the Dynamical Systems Conference Denton, TX, USA. Topology and its Applications. 152 (1-2) 1-1.
  • Journal Article

  • Fishman, L., Urbanski, M., Das, T., Simmons, D. (2024). A variational principle in the parametric geometry of numbers. Advances in Mathematics. 437
  • Bishop, C.J., Lazebnik, K.Y., Urbanski, M. (2023). Equilateral Triangulations and The Postcritical Dynamics of Meromorphic Functions. Mathematische Annalen. 387 1777–1818.
  • Urbanski, M., Pawelec, L. (2023). Estimating Hausdorff Measure for Denjoy Maps. Nonlinearity. 36 (36) 6224-–6238.
  • Fishman, L., Das, T., Urbanski, M., Simmons, D. (2023). Hausdorff dimensions of perturbations of a conformal iterated function system via thermodynamic formalism. Selecta Mathematica. 29 (19) 56.
  • Urbanski, M., Mihailescu, E. (2022). Geometry of measures in random systems with complete connections. Journal of Geometric Analysis (32 (162))
  • Urbanski, M., Mayer, V. (2022). The exact value of Hausdorff dimension of escaping sets of class B of meromorphic functions. Geometric and Functional Analysis. 32 53-80.
  • Urbanski, M., Mihailescu, E. (2021). Smale endomorphisms over graph--directed Markov systems. Ergodic Theory and Dynamical Systems. 41 2508-2541.
  • Urbanski, M., Chousionis, V. (2021). Porosity in Conformal Dynamical Systems. Mathematical Proceedings of the Cambridge Philosophical Society. Published online on April 14, 2021 1-69.
  • Urbanski, M., Das, T., Przytycki, F., Tiozzo, G., Zdunik, A. (2021). Thermodynamic formalism for coarse expanding dynamical systems. Communications in Mathematical Physics. 384 165-199.
  • Urbanski, M., Zdunik, A. (2021). Random non--hyperbolic exponential maps. Journal d'Analyse Mathematique. 143 1-93.
  • Urbanski, M., Das, T., Fishman, L., Simmons, D. (2021). Extremality and Dynamically Defined Measures, Part II. Ergodic Theory and Dynamical Systems. 41 2311-2348.
  • Urbanski, M., Atnip, J. (2020). Critically Finite Random Maps of an Interval. Discrete and Continuous Dynamical Systems. 40 4839-4906.
  • Urbanski, M., Pawelec, L. (2020). Long hitting times for expanding systems. Nonlinearity. 33 942--970.
  • Urbanski, M., Chousionis, V., Leykekhman, D. (2020). On the dimension spectrum of infinite subsystems of continued fractions. Transactions of the American Mathematical Society. 373 1009-1042.
  • Urbanski, M., Mayer, V. (2020). Thermodynamical formalism for entire functions and integral means spectrum of asymptotic tracts. Transactions of the American Mathematical Society. 373 7669–-7711.
  • Urbanski, M., Pawelec, L., Zdunik, A. (2020). Thin annuli property and exponential distribution of return times for weakly Markov systems. Fundamenta Mathematicae. 251 269—-316.
  • Urbanski, M., Mihailescu, E. (2020). Skew product Smale endomorphisms over countable shifts of finite type. Ergodic Theory and Dynamical Systems. 40 3105-3149.
  • Urbanski, M., Mayer, V., Zdunik, A. (2020). Real Analyticity for random dynamics of transcendental functions. Ergodic Theory and Dynamical Systems. 40 490-520.
  • Urbanski, M., Chousionis, V., Leykekhman, D. (2019). Dimension Spectrum of Conformal Graph Directed Markov Systems. Selecta Mathematica. (25) 57.
  • Urbanski, M., Das, T., Fishman, L., Simmons, D. (2019). Badly approximable points on self-affine sponges and the lower Assouad dimension. Ergodic Theory and Dynamical Systems. (39) 638-657.
  • Urbanski, M., Das, T., Fishman, L., Simmons, D. (2018). Badly approximable vectors and fractals defined by conformal dynamical systems. Mathematical Research Letters. 25 437--467.
  • Urbanski, M., Das, T., Fishman, L., Simmons, D. (2018). Extremality and Dynamically Defined Measures, Part I. Selecta Mathematica. 24 2165-2206.
  • Urbanski, M., Mayer, V. (2018). Random Dynamics of Transcendental Functions. Journal d'Analyse Mathematique. 134 201-235.
  • Das, T., Fishman, L., Simmons, D., Urbanski, M. (2017). A variational principle in the parametric geometry of numbers, with applications to metric Diophantine approximation. 355 (8) 835-846.
  • Fishman, L., Urbanski, M., Das, T., Simmons, D. (2017). A variational principle in the parametric geometry of numbers, with applications to metric Diophantine approximation. Comptes Rendus Mathématique. 355 (8) 835-846.
  • Das, T., Simmons, D., Urbanski, M. (2017). Dimension rigidity in conformal structures. Advances in Mathematics. 308 1127-1186.
  • Urbanski, M., Zdunik, A. (2016). Continuity of the Hausdorff Measure of Continued Fractions and Countable Alphabet Iterated Function Systems. Journal de Theorie des Nombres de Bordeaux. 28 (1) 261-286.
  • Mihailescu, E., Urbanski, M. (2016). Dimensional Exactness of Self-Measures for Random Countable Iterated Function Systems with Overlaps. Advances in Mathematics. 298 726-758.
  • Rempe-Gillen, L., Urbanski, M. (2016). NON-AUTONOMOUS CONFORMAL ITERATED FUNCTION SYSTEMS AND MORAN-SET CONSTRUCTIONS. Transactions of the American Mathematical Society. 368 (3) 1979-2017.
  • Mihailescu, E., Urbanski, M. (2016). Overlap Functions for Measures in Conformal Iterated Function Systems. Journal of Statistical Physics. 162 (1) 43-62.
  • Urbanski, M. (2016). Random countable alphabet conformal iterated function systems satisfying the transversality condition. Nonlinearity. 29 (3) 1096-1123.
  • Urbanski, M., Zdunik, A. (2016). Regularity of Hausdorff measure function for conformal dynamical systems. Mathematical Proceedings of the Cambridge Philosophical Society. 160 (3) 537-563.
  • Das, T., Stratmann, B.O., Urbanski, M. (2016). The Bishop-Jones relation and Hausdorff geometry of convex-cobounded limit sets in infinite-dimensional hyperbolic space. Other. 16 (5)
  • Das, T., Simmons, D., Urbanski, M. (2016). TUKIA'S ISOMORPHISM THEOREM IN CAT(-1) SPACES. Other. 41 (2) 659-680.
  • Chousionis, V., Urbanski, M. (2015). A note on weak convergence of singular integrals in metric spaces. Mathematical Research Letters. 22 (1) 11-21.
  • Mayer, V., Urbanski, M. (2015). Countable Alphabet Random Subhifts of Finite Type with Weakly Positive Transfer Operator. Journal of Statistical Physics. 160 (5) 1405-1431.
  • Szostakiewicz, M., Urbanski, M., Zdunik, A. (2015). Fine inducing and equilibrium measures for rational functions of the Riemann sphere. Israel Journal of Mathematics. 210 (1) 399-465.
  • Chousionis, V., Urbanski, M. (2015). Homogeneous Kernels and Self-Similar Sets. Indiana University Mathematics Journal. 64 (2) 411-431.
  • Fishman, L., Simmons, D., Urbanski, M. (2015). Rigidity of limit sets for nonplanar geometrically finite Kleinian groups of the second kind. Geometriae Dedicata. 178 (1) 95-101.
  • Fishman, L., Mance, B., Simmons, D., Urbanski, M. (2015). SHRINKING TARGETS FOR NONAUTONOMOUS DYNAMICAL SYSTEMS CORRESPONDING TO CANTOR SERIES EXPANSIONS. Bulletin of the Australian Mathematical Society. 92 (2) 205-213.
  • Fishman, L., Simmons, D., Urbanski, M. (2014). Diophantine approximation in Banach spaces. Journal de Theorie des Nombres de Bordeaux. 26 (2) 363-384.
  • Fishman, L., Simmons, D., Urbanski, M. (2014). Diophantine properties of measures invariant with respect to the Gauss map. Other. 122 289-315.
  • Skorulski, B., Urbanski, M. (2014). Finer fractal geometry for analytic families of conformal dynamical systems. Other. 29 (3) 369-398.
  • Mihailescu, E., Urbanski, M. (2014). Measure-theoretic degrees and topological pressure for non-expanding transformations. Journal of Functional Analysis. 267 (8) 2823-2845.
  • Simmons, D., Urbanski, M. (2014). RELATIVE EQUILIBRIUM STATES AND DIMENSIONS OF FIBERWISE INVARIANT MEASURES FOR RANDOM DISTANCE EXPANDING MAPS. Other. 14 (1)
  • Szostakiewicz, M., Urbanski, M., Zdunik, A. (2014). Stochastics and thermodynamics for equilibrium measures of holomorphic endomorphisms on complex projective spaces. Other. 174 (1) 141-162.
  • Muir, S., Urbanski, M. (2014). Thermodynamic formalism for a modified shift map. Other. 14 (2)
  • Szarek, T., Urbanski, M., Zdunik, A. (2013). CONTINUITY OF HAUSDORFF MEASURE FOR CONFORMAL DYNAMICAL SYSTEMS. Discrete and Continuous Dynamical Systems. 33 (10) 4647-4692.
  • Mihailescu, E., Urbanski, M. (2013). Entropy Production for a Class of Inverse SRB Measures. Journal of Statistical Physics. 150 (5) 881-888.
  • Urbanski, M., Zdunik, A. (2013). Equilibrium measures for holomorphic endomorphisms of complex projective spaces. Fundamenta Mathematicae. 220 (1) 23-69.
  • Mayer, V., Skorulski, B., Urbanski, M. (2013). REGULARITY AND IRREGULARITY OF FIBER DIMENSIONS OF NON-AUTONOMOUS DYNAMICAL SYSTEMS. Other. 38 (2) 489-514.
  • Sumi, H., Urbanski, M. (2013). Transversality family of expanding rational semigroups. Advances in Mathematics. 234 697-734.
  • Sumi, H., Urbanski, M. (2012). BOWEN PARAMETER AND HAUSDORFF DIMENSION FOR EXPANDING RATIONAL SEMIGROUPS. Discrete and Continuous Dynamical Systems. 32 (7) 2591-2606.
  • Skorulski, B., Urbanski, M. (2012). Dynamical rigidity of transcendental meromorphic functions. Nonlinearity. 25 (8) 2337-2348.
  • Mihailescu, E., Urbanski, M. (2011). HAUSDORFF DIMENSION OF THE LIMIT SET OF CONFORMAL ITERATED FUNCTION SYSTEMS WITH OVERLAPS. Proceedings of the American Mathematical Society. 139 (8) 2767-2775.
  • Sumi, H., Urbanski, M. (2011). MEASURES AND DIMENSIONS OF JULIA SETS OF SEMI-HYPERBOLIC RATIONAL SEMIGROUPS. Discrete and Continuous Dynamical Systems. 30 (1) 313-363.
  • Roy, M., Urbanski, M. (2011). RANDOM GRAPH DIRECTED MARKOV SYSTEMS. Discrete and Continuous Dynamical Systems. 30 (1) 261-298.
  • Akter, H., Urbanski, M. (2011). REAL ANALYTICITY OF HAUSDORFF DIMENSION OF JULIA SETS OF PARABOLIC POLYNOMIALS f(lambda)(z) = z(1-z-lambda z(2)). Illinois Journal of Mathematics. 55 (1) 157-184.
  • Mayer, V., Skorulski, B., Urbanski, M. (2011). Real Analyticity of Pressure. Other. Lecture Notes in Mathematics. 2036 93-108.
  • Das, T., Urbanski, M. (2011). The geometry of Baire spaces. Other. 26 (4) 537-567.
  • Urbanski, M. (2010). Analytic Families of Semihyperbolic Generalized Polynomial-Like Mappings.
  • with V. Mayer. (2010). Ergodic properties of sub-hyperbolic functions with polynomial Schwarzian derivative.
  • with T. Szarek and M. Sleczka. (2010). On Stability of Velocity Vectors for Some Passive Tracer Models,.
  • with H. Sumi. (2010). Real Analyticity of Hausdorff Dimension for Expanding Rational Semigroups.
  • with E. Mihailescu. (2010). Relations between stable dimension and the preimage counting function on basic sets with overlaps.
  • with G. Havard and M. Zinsmeister. (2010). Variations of Hausdorff Dimension in the exponential family.
  • Urbanski, M. (2009). Geometric Rigidity for Class S of Transcendental Meromorphic Functions whose Julia Sets are Jordan Curves.
  • with R. D. Mauldin and T. Szarek. (2009). Graph Directed Markov Systems on Hilbert Spaces.
  • with M. Roy and H. Sumi. (2009). Lambda-topology vs. pointwise topology.
  • with M. Roy. (2009). Multifractal analysis for conformal graph directed Markov systems.
  • with H. Sumi. (2009). The Equilibrium States for Semigroups of Rational Maps, Monatshefte fur Math. 156 (2009), 371-390.
  • Urbanski, M. (2009). Transfinite Hausdorff Dimension.
  • with M. Roy and H. Sumi. (2008). Analytic Families of Holomorphic IFS.
  • with M. Ch. Wolf. (2008). Ergodic Theory of Parabolic Horseshoes.
  • with J. Kotus. (2008). Fractal Measures and Ergodic Theory of Transcendental Meromorphic Functions.
  • with V. Mayer. (2008). Geometric Thermodynamical Formalism and Real Analyticity for Meromorphic Functions of Finite Order.
  • with A. Bis. (2008). Geometry of Markov Systems and Codimension-One Foliations.
  • with J. Kotus. (2008). Hausdorff dimension of radial and escaping points for transcendental meromorphic functions.
  • with E. Mihailescu. (2008). Inverse pressure estimates and the independence of stable dimension for non-invertible maps.
  • with M. Roy. (2008). Real Analyticity of Hausdorff Dimension for Higher Dimensional Graph Directed Markov Systems.
  • with E. Mihailescu. (2008). Transversal Families of Skew-Product Axiom A Endomorphisms.
  • Urbanski, M., Jenkinson, O., Mauldin, D. (2007). Ergodic optimization for non-compact dynamical systems. Dynamical Systems. 22 379-388.
  • with V. Mayer. (2007). Fractal Measures for Meromorphic Functions of Finite Order.
  • with A. Zdunik. (2007). Geometry and ergodic theory of non-hyperbolic exponential maps.
  • with M. Kessebohmer. (2007). Higher-Dimensional Multifractal Value Sets for Infinite Graph Directed Markov Systems.
  • with A. Zdunik. (2007). Instability of Exponential Collet - Eckmann Maps.
  • with Alexander M. Davie and A. Zdunik. (2007). Maximizing Measures on Metrizable Non-Compact Spaces.
  • with B. Stratmann. (2007). Pseudo-Markov Systems and Infinitely Generated Schottky Groups.
  • Urbanski, M. (2007). Recurrence Rates for Loosely Markov Dynamical Systems.
  • with B. Stratmann. (2006). Diophantine Extremality of the Patterson Measure.
  • with O. Jenkinson and D. Mauldin. (2006). Ergodic optimization for countable alphabet subshifts of infinite type.
  • Urbanski, M. (2006). Finer Diophantine and regularity properties of 1-Dimensional Parabolic IFS.
  • with J. Kotus. (2006). Geometric rigidity of transcendental meromorphic functions.
  • with J. Kotus. (2006). Geometry and dynamics of some meromorphic functions.
  • with B. Karpinska. (2006). How points escape to innity under exponential maps.
  • with M. Zinsmeister. (2006). Parabolic Implosion and Julia-Lavaurs Sets in the ExponentialFamily.
  • with A. Bis. (2006). Some remarks on topological entropy of a semigroup of countinuous maps.
  • with J. Kotus. (2006). Virtual Centers of Hyperbolic components in the tangent family;Hausdorff Dimension Outlook.
  • Urbanski, M. (2005). Diophantine approximation and self-conformal measures. Journal of Number Theory. 110 (2) 219-235.
  • Urbanski, M. (2005). Diophantine approximation for conformal measures of one-dimensional iterated function systems. Compositio Mathematica. 141 (4) 869-886.
  • Urbanski, M. (2005). Diophantine Approximation for Conformal Measures of One-Dimensional IteratedFunction Systems.
  • Urbanski, M. (2005). Diophantine Approximation of Self-Conformal Measures.
  • Mihailescu, E., Urbanski, M. (2005). Estimates for the stable dimension for holomorphic maps. Houston Journal of Mathematics. 31 (2) 367-389.
  • Mayer, V., Urbanski, M. (2005). Exponential elliptics give dimension two. Illinois Journal of Mathematics. 49 (1) 291-294.
  • with V. Mayer. (2005). Exponential elliptics give dimension two.
  • with V. Mayer. (2005). Gibbs and equilibrium measures for elliptic functions.
  • Mayer, V., Urbanski, M. (2005). Gibbs and equilibrium measures for elliptic functions. Mathematische Zeitschrift. 250 (3) 657-683.
  • with M. Roy. (2005). Regularity properties of Hausdorff dimension in conformal infiniteIFS.
  • Roy, M., Urbanski, M. (2005). Regularity properties of Hausdorff dimension in infinite conformal iterated function systems. Ergodic Theory and Dynamical Systems. 25 1961-1983.
  • with J. Kotus. (2005). The dynamics and geometry of the Fatou functions.
  • Kotus, J., Urbanski, M. (2005). The dynamics and geometry of the Fatou functions. Discrete and Continuous Dynamical Systems. 13 (2) 291-338.
  • Jenkinson, O., Mauldin, R., Urbanski, M. (2005). Zero temperature limits of Gibbs-equilibrium states for countable alphabet subshifts of finite type. Journal of Statistical Physics. 119 (3-4) 765-776.
  • with J. Kotus. (2004). Geometry and ergodic theory of non-recurrent elliptic functions.
  • Mihailescu, E., Urbanski, M. (2004). Inverse topological pressure with applications to holomorphic dynamics of several complex variables. Communications in Contemporary Mathematics. 6 (4) 653-679.
  • Stratmann, B., Urbanski, M. (2004). Metrical diophantine analysis for tame parabolic iterated function systems. Pacific Journal of Mathematics. 216 (2) 361-392.
  • with B. Stratmann. (2004). Multifractal analysis for parabolically semihyperbolic generalizedpolynomial-like maps.
  • Urbanski, M., Zdunik, A. (2004). Real analyticity of Hausdorff dimension of finer Julia sets of exponential family. Ergodic Theory and Dynamical Systems. 24 279-315.
  • Urbanski, M., Wolf, C. (2004). SRB measures for Axiom A endomorphisms. Mathematical Research Letters. 11 (5-6) 785-797.
  • Urbanski, M., Zdunik, A. (2004). The parabolic map f1/e(z) = (1)/(e)e(z). Other. 15 (3) 419-433.
  • Roy, M., Urbanski, M. (2003). Conformal families of measures for fibred systems. Other. 140 (2) 135-145.
  • Kotus, J., Urbanski, M. (2003). Existence of invariant measures for transcendental subexpanding functions. Mathematische Zeitschrift. 243 (1) 25-36.
  • Mayer, V., Urbanski, M. (2003). Finer geometric rigidity of limit sets of conformal IFS. Proceedings of the American Mathematical Society. 131 (12) 3695-3702.
  • with V. Mayer. (2003). Finer Geometric Rigidity of Limit Sets of Conformal IFS. Proceedings of the American Mathematical Society. 131 3695‑3702.
  • Kotus, J., Urbanski, M. (2003). Hausdorff dimension and Hausdorff measures of Julia sets of elliptic functions. Bulletin of the London Mathematical Society. 35 269-275.
  • Mihailescu, E., Urbanski, M. (2003). Holomorphic maps for which the unstable manifolds depend on prehistories. Discrete and Continuous Dynamical Systems. 9 (2) 443-450.
  • Urbanski, M. (2003). Measures and dimensions in conformal dynamics. Bulletin of the American Mathematical Society. 40 (3) 281-321.
  • Jenkinson, O., Gonzalez, L., Urbanski, M. (2003). On transfer operators for continued fractions with restricted digits. Other. 86 755-778.
  • Urbanski, M. (2003). Optimal periodic orbits for non-recurrent rational functions.
  • Maume-Deschamps, V., Schmitt, B., Urbanski, M., Zdunik, A. (2003). Pressure and recurrence. Fundamenta Mathematicae. 178 (2) 129-141.
  • Stratmann, B., Urbanski, M. (2003). Real analyticity of topological pressure for parabolically semihyperbolic generalized polynomial-like maps. Other. 14 (1) 119-134.
  • Mauldin, R., Urbanski, M. (2003). The doubling property of conformal measures of infinite iterated function systems. Journal of Number Theory. 102 (1) 23-40.
  • Urbanski, M., Zdunik, A. (2003). The finer geometry and dynamics of the hyperbolic exponential family. Michigan Mathematical Journal. 51 (2) 227-250.
  • Urbanski, M. (2003). Thermodynamic formalism, topological pressure, and escape rates for critically non-recurrent conformal dynamics. Fundamenta Mathematicae. 176 (2) 97-125.
  • Kotus, J., Urbanski, M. (2002). Conformal, geometric and invariant measures for transcendental expanding functions. Mathematische Annalen. 324 (3) 619-656.
  • Urbanski, M. (2002). Diophantine analysis of conformal iterated function systems. Other. 137 (4) 325-340.
  • Mauldin, R., Urbanski, M. (2002). Fractal measures for parabolic IFS. Advances in Mathematics. 168 (2) 225-253.
  • Heinemann, S., Urbanski, M. (2002). Hausdorff dimension estimates for infinite conformal IFSs. Nonlinearity. 15 (3) 727-734.
  • Urbanski, M., Zdunik, A. (2002). Hausdorff dimension of harmonic measure for self-conformal sets. Advances in Mathematics. 171 (1) 1-58.
  • Stratmann, B., Urbanski, M. (2002). Jarnik and Julia; A Diophantine analysis for parabolic rational maps for geometrically finite Kleinian groups with parabolic elements. Mathematica Scandinavica. 91 (1) 27-54.
  • Urbanski, M. (2002). The Diophanitne analysis of conformal iterated function systems.
  • Bedford, T., Fisher, A., Urbanski, M. (2002). The scenery flow for hyperbolic Julia sets. Other. 85 467-492.
  • with T. Bedford and A. Fisher. (2002). The scenery ow for hyperbolic Julia sets. Proceedings of the London Mathematical Society.
  • Hanus, P., Mauldin, R., Urbanski, M. (2002). Thermodynamic formalism and multifractal analysis of conformal infinite iterated function systems. Acta Mathematica Hungarica. 96 (1-2) 27-98.
  • with M. Zinsmeister. (2001). Continuity of Hausdor dimension of Julia-Lavaurs sets asa function of the phase.
  • Urbanski, M., Zinsmeister, M. (2001). Geometry of hyperbolic Julia-Lavaurs sets. Other. 12 (2) 273-292.
  • Mauldin, R., Urbanski, M. (2001). Gibbs states on the symbolic space over an infinite alphabet. Israel Journal of Mathematics. 125 93-130.
  • Simon, K., Solomyak, B., Urbanski, M. (2001). Hausdorff dimension of limit sets for parabolic IFS with overlaps. Pacific Journal of Mathematics. 201 (2) 441-478.
  • Simon, K., Solomyak, B., Urbanski, M. (2001). Invariant measures for parabolic IFS with overlaps and random continued fractions. Transactions of the American Mathematical Society. 353 (12) 5145-5164.
  • Solomyak, B., Urbanski, M. (2001). L-q densities for measures associated with parabolic IFS with overlaps. Indiana University Mathematics Journal. 50 (4) 1845-1866.
  • with B. Solomyak. (2001). Lq-densities for some random continued fractions and parabolicIFS with overlaps.
  • Urbanski, M. (2001). Porosity in conformal infinite iterated function systems. Journal of Number Theory. 88 (2) 283-312.
  • Przytycki, F., Urbanski, M. (2001). Porosity of Julia sets of non-recurrent and parabolic Collet-Eckmann rational functions. Other. 26 (1) 125-154.
  • Mauldin, R., Przytycki, F., Urbanski, M. (2001). Rigidity of conformal iterated function systems. Compositio Mathematica. 129 (3) 273-299.
  • Mauldin, R., Mayer, V., Urbanski, M. (2001). Rigidity of connected limit sets of conformal IFSs. Michigan Mathematical Journal. 49 (3) 451-458.
  • Urbanski, M. (2001). Rigidity of multi-dimensional conformal iterated function systems. Nonlinearity. 14 (6) 1593-1610.
  • with D. Mauldin. (2001). V. Mayer Rigidity of connected limit sets of conformal IFS.
  • with B. Stratmann and M. Zinsmeister. (2001). Well-approximable points for Julia sets withparabolic and critical points.
  • Fisher, A., Urbanski, M. (2000). On invariant line fields. Bulletin of the London Mathematical Society. 32 555-570.
  • with D. Mauldin. (2000). Parabolic iterated function systems.
  • Mauldin, R., Urbanski, M. (2000). Parabolic iterated function systems. Ergodic Theory and Dynamical Systems. 20 1423-1447.
  • Stratmann, B., Urbanski, M. (2000). The geometry of conformal measures for parabolic rational maps. Mathematical Proceedings of the Cambridge Philosophical Society. 128 141-156.
  • with B. Stratmann. (2000). The geometry of conformal measures for parabolic rationalmaps. Mathematical Proceedings of the Cambridge Philosophical Society.
  • with P. Hanus. (1999). A new class of positive recurrent functions, \Geometry and Topologyin dynamics".
  • Mauldin, R., Urbanski, M. (1999). Conformal iterated function systems with applications to the geometry of continued fractions. Transactions of the American Mathematical Society. 351 (12) 4995-5025.
  • with F. Przytycki. (1999). Rigidity of tame rational functions.
  • with P. Hanus. (1998). Complex continued fractions with restricted entries.
  • Denker, M., Mauldin, R., Nitecki, Z., Urbanski, M. (1998). Conformal measures for rational functions revisited. Fundamenta Mathematicae. 157 (2-3) 161-173.
  • Mauldin, R., Urbanski, M. (1998). Dimension and measures for a curvilinear Sierpinski gasket or Apollonian packing. Advances in Mathematics. 136 (1) 26-38.
  • Urbanski, M. (1998). Hausdor measures versus equilibrium states of conformal infinite iterated functionsystems.
  • with D. Mauldin. (1998). On the uniqueness of the density for the invariant measure in aninfinite hyperbolic iterated function system.
  • with P. Hanus. (1998). Rigidity of infinite iterated function systems.
  • Urbanski, M. (1997). Geometry and ergodic theory of conformal non-recurrent dynamics. Ergodic Theory and Dynamical Systems. 17 1449-1476.
  • Mauldin, R., Urbanski, M. (1996). Dimensions and measures in infinite iterated function systems. Proceedings of the London Mathematical Society. 73 105-154.
  • Denker, M., Przytycki, F., Urbanski, M. (1996). On the transfer operator for rational functions on the Riemann sphere. Ergodic Theory and Dynamical Systems. 16 255-266.
  • Urbanski, M. (1996). Parabolic Cantor sets. Fundamenta Mathematicae. 151 (3) 241-277.
  • Stratmann, B., Urbanski, M. (1996). The box-counting dimension for geometrically finite Kleinian groups. Fundamenta Mathematicae. 149 (1) 83-93.
  • Urbanski, M. (1995). A new transnite dimension for metrizable spaces.
  • with M. Denker, Z. Nitecki. (1995). Conformal measures and S-Unimodal maps.
  • with L. Zamboni. (1994). Circle Maps, Measured Laminations, and Free Group Actions onIR- Trees.
  • with F. Hofbauer. (1994). Fractal properties of invariant subsets for piecewise monotonicmaps on the interval.
  • with D. Mauldin. (1994). Jordan curves as repellors.
  • Urbanski, M. (1994). Rational functions with no recurrent critical points.
  • with M. Denker. (1994). Relating Hausdor measures and harmonic measures on parabolicJordan curves.
  • with J. Aaronson, M. Denker. (1993). Ergodic theory for Markov bered systems and parabolic rational maps.
  • with L. Zamboni. (1993). On free actions on -trees. Mathematical Proceedings of the Cambridge Philosophical Society.
  • with M. Denker. (1992). Geometric measures for parabolic rational maps.
  • with M. Denker. (1992). The Capacity of parabolic Julia sets.
  • with M. Denker. (1991). Ergodic theory of equilibrium states for rational maps.
  • with F. Przytycki and (with A. Zdunik). (1991). Harmonic, Gibbs and Hausdorff measureson repellers for holomorphic maps II.
  • with M. Denker. (1991). Hausdor and conformal measures on Julia sets with a rationallyindifferent periodic point.
  • with M. Denker. (1991). On absolutely continuous invariant measures for expansive rationalmaps with rationally indifferent periodic points.
  • Urbanski, M. (1991). On Hausdor dimension of Julia set with a rationally indifferent periodic point.
  • with M. Denker. (1991). On Hausdorff measures on Julia sets of subexpanding rationalmaps.
  • with M. Denker. (1991). On Sullivan's conformal measures for rational maps of the Riemannsphere.
  • with M. Denker. (1991). On the existence of conformal measures.
  • Urbanski, M. (1991). The Hausdorff dimension of the set of points with non - dense orbit under a hyperbolicdynamical system.
  • with M. Denker and G. Keller. (1990). On the uniqueness of equilibrium states for piecewise monotone maps.
  • with T. Bedford. (1990). The box and Hausdorff dimension of self-affine sets.
  • Urbanski, M. (1990). The Hausdorff dimension of the graphs of continuous self-affine functions. Proceedings of the American Mathematical Society.
  • Urbanski, M. (1990). The probability distribution and Hausdorff dimension of self-affine functions.
  • with F. Przytycki and (with A. Zdunik). (1989). Harmonic, Gibbs and Hausdor measureson repellers for holomorphic maps I.
  • Urbanski, M. (1989). Hausdorff dimension of invariant subsets for endomorphisms of the circle with anindifferent fixed point.
  • with F. Przytycki. (1989). On Hausdor dimension of some fractal sets.
  • Urbanski, M. (1987). Invariant subsets of expanding mappings of the circle.
  • Urbanski, M. (1986). Hausdor dimension of invariant sets for expanding maps of a circle.
  • Urbanski, M. (1985). On a capacity of a continuum with non-dense orbit under a hyperbolic toral automorphism.
  • Monograph

  • Urbanski, M., Pollicott, M. (2021). Asymptotic Counting in Conformal Dynamical Systems. Memoirs of the American Mathematical Society. 1-139. Memoirs of American Mathematical Society.
  • Urbanski, M., Chousionis, V., Tyson, J. (2020). Conformal graph directed Markov systems on Carnot groups. Memoirs of the American Mathematical Society. 266 1-155. Memoirs of the American Mathematical Society.
  • Urbanski, M., Pollicott, M. (2018). Open Conformal Systems and Perturbations of Perron-Frobenius Operators. 2206 201. Springer's Lecture Notes in Mathematics.
  • Urbanski, M., Fishman, L., Simmons, D. (2018). Diophantine Approximation and the Geometry of Limit Sets in Gromov Hyperbolic Metric Spaces. Memoirs of the American Mathematical Society. 254 (Issue: 1215) 1-137. Memoirs of American Mathematical Society.
  • Mayer, V., Skorulski, B., Urbanski, M. (2011). Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry Introduction. Springer's Lecture Notes in Mathematics. 2036 112.
  • with V. Mayer. (2010). Thermodynamical Formalism and Multifractal Analysis for Meromorphic Functions of Finite Order. 105.

Presentations Given

    Design Work

  • Urbanski, M. (Author & Presenter), Dynamical Systems Seminar in Penn State, Orbit Counting in Conformal Dynamical Systems, Penn State University, Penn State, United States of America. (2017 - 2017).
  • Invited Talk

  • Urbanski, M. (Author & Presenter), Thermodynamic Formalism for Random Dynamical Systems, Thermodynamic Formalism for Symbolic Open Systems via Singular Perturbations, MATRIX Institute of Melbourne, Australia, Creswick, Australia, Australia. (2023 - 2023).
  • Urbanski, M. (Author & Presenter), Geometry of deterministic and random fractals, Hausdorff Dimension of Escaping Sets for Class B Meromorphic Functions, Budapest, Hungary. (2022 - 2022).
  • Urbanski, M. (Author & Presenter), Zoom seminar lecture for the Conformal Dynamics and Groups seminar, Hausdorff Dimension of Escaping Set for Class B of Meromorphic Functions, Peking, China. (2022 - 2022).
  • Urbanski, M. (Author), Dynamical Section of the Zoom AMS Regional Conference at Atlanta, Georgia, Hausdorff Dimension of Escaping Sets for Class B of Meromorphic Functions, AMS, Atlanta, United States of America. (2021 - 2021).
  • Urbanski, M. (Author & Presenter), Zoom Conference "Dynamics of (Semi-)Group Actions", Lod\'z, Poland, Subhyperbolic Rational Semigroups, Lodz, Poland. (2021 - 2021).
  • Urbanski, M. (Author & Presenter), Zoom Seminar Lecture for the Dynamics Group at the University of Sydney, Australia, Conformal Measures and Thermodynamic Formalism for Non-Hyperbolic Random Exponential Functions, University of Sydney, Australia, Australia. (2020 - 2020).
  • Urbanski, M. (Presenter), Dynamical Systems and Ergodic Theory at the sectional AMS Meeting #1153, Dimension Spectrum of Conformal Iterated Function Systems, University of North Texas, UC Riverside, CA, United States of America. (2019 - 2019).
  • Urbanski, M. (Presenter), Dynamics of (Semi-)Group Actions, Ergodic Theory and Fractal Geometry of Semi-Hyperbolic Finitely Generated Rational Semigroups, University of North Texas; University of Lodz, University of Lodz n Lodz, Poland, Poland. (2019 - 2019).
  • Urbanski, M. (Presenter), Thermodynamic Formalism - Applications to Geometry, Number Theory, and Stochastics, Random Non--Hyperbolic Exponential Maps, Mittag-Leffler Institute, Mittag-Leffler Institute, Stockholm, Sweden, Sweden. (2019 - 2019).
  • Urbanski, M. (Presenter), Thermodynamic Formalism: Ergodic Theory and Geometry, Dimension Spectrum in Conformal Dynamical Systems, University of North Texas; University of Warwick, University of Warwick; Coventry, UK, United Kingdom. (2019 - 2019).
  • Urbanski, M. (Presenter), Thermodynamic Formalism: Modern Techniques in Smooth Ergodic Theory, Thermodynamic Formalism in Transcendental Dynamics, CIRM, Luminy (Marseilles), France, France. (2019 - 2019).
  • Urbanski, M. (Presenter), Geometry Seminar at Caltech, CA, Dimension Spectrum in Conformal Dynamical Systems, California Institute of Technology, Caltech, Pasadena, CA, United States of America. (2019 - 2019).
  • Urbanski, M. (Author & Presenter), Resonances of complex dynamics, Thermodynamic formalism and iterated function systems in transcendental dynamics, International Centre for Mathematical Sciences, Edinburgh, United Kingdom. (2018 - 2018).
  • Urbanski, M. (Author & Presenter), AMS Meeting at Riverside, Thermodanamic formalism and integral means for transcendental entire functions, AMS Meeting at Riverside, CA, United States of America. (2017 - 2017).
  • Urbanski, M. (Author & Presenter), Center for Dynamics and Geometry Colloquium in Penn State, Thermodanamic formalism and integral means for transcendental entire functions, Penn State University, Penn State, United States of America. (2017 - 2017).
  • Urbanski, M. (Author & Presenter), Conference on Fractals, Harmonic Analysis, and Geometric Applications, Orbit Counting in Conformal Dynamical Systems; with applications to Apollonian packings, Ohio State University, Ohio State, Columbus, United States of America. (2017 - 2017).
  • Urbanski, M. (Author & Presenter), Colloquium Lecture for the Department of Mathematics of the University of Osaka, Exponential distribution in weakly markov systems, Osaka University, Osaka, Japan. (2016 - 2016).
  • Urbanski, M. (Author & Presenter), Dynamical Systems Seminar, Exponential Law in Dynamical Systems, University of Kyoto, Kyoto,, Japan. (2016 - 2016).
  • Urbanski, M. (Author & Presenter), Dynamics Workshop in Osaka, Transfer operators in conformal dynamical systems, Osaka University, Osaka, Japan. (2016 - 2016).
  • Urbanski, M. (Author & Presenter), Dynamical Systems Seminar in the University of Warsaw, Thermodynamic Formalism for for countable subshifts of finite type, Institute of Mathematics of the University of Warsaw, Warsaw, Poland. (2016 - 2016).
  • Urbanski, M. (Author & Presenter), Dynamical Systems Seminar of the Mathematical Institute of the Polish Academy of Science, Extremal measures in hyperbolic dynamical systems, Mathematical Institute of the Polish Academy of Science, Warsaw, Poland. (2016 - 2016).
  • Urbanski, M. (Author & Presenter), Geometry Seminar, Geometric Rigidity in Conformal Dynamical Syestems, University of Lille, Lille, France. (2016 - 2016).
  • Urbanski, M. (Author & Presenter), Scientific Seminar, Geometric Rigidity in Conformal Dynamical Syestems, Institute des Hautes Etudes Scientifiques, Bures --sur-- Ivette, Paris, France. (2016 - 2016).
  • Urbanski, M. (Author & Presenter), Ergodic Theory and Holomorphic Dynamics, Random Meromorphic Functions, Erwin Schroedinger Institute (ESI), Vienna, Austria, Austria. (2015 - 2015).
  • Urbanski, M. (Author & Presenter), Topics in Analysis and Holomorphic Dynamics, Random Meromorphic Functions, Simons Foundation, Warsaw, Poland, Poland. (2015 - 2015).
  • Urbanski, M. (Author & Presenter), Dynamical Systems Seminar in the Mathematical Institute of the Polish Academy of Science, Diophantine Approximation in hyperbolic Dynamical Systems, Mathematical Institute of the Polish Academy of Science in Warsaw, Warsaw, Poland, Poland. (2015 - 2015).
  • Urbanski, M. (Author & Presenter), 49th Annual Topology and Dynamical Systems Conference, Random Distance Expanding Dynamical Systems, NSF, Bowling Green, Ohio, United States of America. (2015 - 2015).
  • Urbanski, M. (Presenter), Conference in honor of 60th Birthday Anniversary of Prof. Janina Kotus, Research of Prof. Janina Kotus, Warsaw University of Technology, Warsaw, Poland, Poland. (2015 - 2015).
  • Urbanski, M. (Author & Presenter), Dynamical Systems Seminar in Bremen, Random Subshiftts of finite type, University of Bremen, Bremen, germany, Germany. (2015 - 2015).
  • Urbanski, M. (Author & Presenter), ''Differentiable Ergodic Theory, Dimension Theory and Stable Foliations'', Extremality of Patterson-Sullivan Measures, German NSF, Oberwolfach, Germany, Germany. (2014 - 2014).
  • Urbanski, M. (Author & Presenter), Ergodic Theory and Dynamical Systems, Geometric Rigidity in Conformal Dynamical Syestems, University of Torun, Torun, Poland, Poland. (2014 - 2014).
  • Urbanski, M. (Author & Presenter), Analysis Seminar Lecture in Rice University, Dimension rigidity of rational functions on the Riemann sphere, Rice University, Houston, TX, United States of America. (2013 - 2013).
  • Urbanski, M. (Author & Presenter), Colloquium Lecture in the University of Houston, Continuity of numerical values of Hausdorff measures, University of Houston, Houston, TX, United States of America. (2013 - 2013).
  • Urbanski, M. (Author & Presenter), The role of complex analysis in complex dynamics, The Dynamics of Meromorphic functions with Polynomial Schwarzian Derivative, University of Edinburgh, Edinburgh, UK, United Kingdom. (2013 - 2013).
  • Urbanski, M. (Author & Presenter), Conference “Dynamics of Groups and Rational Maps, Phase transitions in meromosrphic dynamics, IPAM, IMPAM, UCLA, Los Angeles, CA, United States of America. (2013 - 2013).
  • Urbanski, M. (Author & Presenter), Analysis Seminar Lecture in Urbana-Champaign, Dimension rigidity of rational functions on the Riemann sphere, University of Urbana-Champaign, Urbana-Champaign, IL, United States of America. (2013 - 2013).
  • Urbanski, M. (Presenter), RTG Conference, Denton, Research contribution of Dan Mauldin, NSF, Denton, TX, United States of America. (2012 - 2012).
  • Urbanski, M. (Author & Presenter), 1. Ergodic Theory and Dynamical Systems: Prospects and Perspectives, Graph directed markov systems and countable alphabet subshifts of finite type, University of Warwick, Coventry, UK, United Kingdom. (2012 - 2012).
  • Urbanski, M. (Author & Presenter), Ergodic Methods in Dynamics, Thermodynamic Formalism of Exponential Functions, Banach Center, Będlewo, Poland, Poland. (2012 - 2012).
  • Urbanski, M. (Author & Presenter), 2012 Spring Western Section AMS Meeting; Special Session on Geometry and Analysis on Fractal Spaces, Multifractal Analysis of Meromorphic Functions, AMS, Manoa, Hawai, United States of America. (2012 - 2012).
  • Urbanski, M. (Author & Presenter), Geometry Seminar of the Rice University, Dynamics of meromorphic functions of finite order, Rice University, Houston, TX, United States of America. (2011 - 2011).
  • Urbanski, M. (Author & Presenter), Dimension Theory in Dynamical Systems, Transfinite Hausdorff Dimension, University of Warwick, Coventry, UK, United Kingdom. (2011 - 2011).
  • Urbanski, M. (Author & Presenter), 45th Spring Conference on Topology and Dynamical Systems in March 2011, Geometric Rigidity of Conformal Iterated Function Systems, NSF, Tyler, TX, United States of America. (2011 - 2011).
  • Urbanski, M. (Author & Presenter), Dynamical Systems Seminar in the University of Warsaw, Transfinite Hausdorff Dimension, University of Warsaw, Warsaw, Poland, Poland. (2010 - 2010).
  • Urbanski, M. (Author & Presenter), IMPAN-CODY Dynamical Seminar, Graph Directed Markov Systems, Real Analyticity, and Nice Sets in Transcendental Dynamics, IMPAN & CODY, Warsaw, Poland, Poland. (2010 - 2010).
  • Urbanski, M. (Author & Presenter), Dynamics Seminar of the University of Bremen, Thermodynamic Formalism of Meromorphic Functions, University of Bremen, Bremen, Germany, Germany. (2010 - 2010).
  • Keynote/Plenary Address

  • Urbanski, M. (Author & Presenter), Rice Dynamics Meeting, Geometric Rigidity in Conformal Dynamical Systems, Rice University, Houston, texas, United States of America. (2014 - 2014).
  • Urbanski, M. (Author & Presenter), International Conference & Workshop on Fractals & Wavelets, The theory of conformal graph Directed Markov systems, University of Cochin, Cochi, Kelala, India, India. (2013 - 2013).
  • Urbanski, M. (Author & Presenter), 2011 Fractals and Related Fields II Conference, Transfinite Hausdorff Dimensio, French NSF, Porquerolles Island, France, France. (2011 - 2011).
  • Urbanski, M. (Author & Presenter), Bicentennial Workshop on Dynamical Systems in San Pedro de Atacama, Ergodic Theory and Geometry of Transcendental Meromorphic Functions (Extension of the minicourse delivered in North Bay), Chle NSF, San Pedro de Atacama, Chile, Chile. (2010 - 2010).
  • Urbanski, M. (Author & Presenter), Workshops on Recent Advances in Topological and Measure-Theoretic Methods in Dynamical Systems, Ergodic Theory and Geometry of Transcendental Meromorphic Functions, NSF, Nipissing University, North Bay, Canada, Canada. (2010 - 2010).
  • Lecture

  • Urbanski, M. (Author & Presenter), Dynamical Systems Seminar at UNT, Ruelle's Operator and Conformal Measures with Applications in Fractal Geometry and NumberTheory, UNT, Denton, TX, United States of America. (2023 - 2023).
  • Urbanski, M. (Author & Presenter), Modern Holomorphic Dynamics and Related Fields, Thermodynamic Formalism for Symbolic Open Systems via Singular Perturbations, University of Warsaw, Poland, Warsaw, Poland, Poland. (2023 - 2023).
  • Urbanski, M. (Author & Presenter), Seminar Lecture at the Queensland University in Brisbane, Australia, Hausdorff dimension of Escaping sets for Class $\cB$ of Meromorphic Functions, Queensland University in Brisbane, Australia, Brisbane, Australia, Australia. (2023 - 2023).
  • Urbanski, M. (Author & Presenter), Seminar Lecture at the University of New South Wales in Sydney, Australia, Dimension Spectrum in Conformal Dynamical Systems, University of New South Wales in Sydney, Australia, New South Wales in Sydney, Australia, Australia. (2023 - 2023).
  • Urbanski, M. (Author & Presenter), Sierpinski Medal Award, Ruelle's Operator and Conformal Measures with Applications in Fractal Geometry and NumberTheory, Polish Mathematical Society and University of Warsaw, Poland, Warsaw, Poland, Poland. (2023 - 2023).
  • Urbanski, M. (Author & Presenter), Thermodynamic Formalism for Geodesic Flow, Thermodynamic Formalism for Symbolic Open Systems via Singular Perturbations, BIRS Institute in Kelowna, Canada, Kelowna, Canada, Canada. (2023 - 2023).
  • Urbanski, M. (Author & Presenter), Zoom seminar lecture for the Conformal Dynamics and Groups seminar, Hausdorff dimension of escaping sets for meromorphic functions, Conformal Dynamics and Groups seminar at the Peking University, Peking University, China, China. (2022 - 2022).
  • Urbanski, M. (Author & Presenter), UTD Colloquium, Thermodynamic Formalism in Transcendental Dynamics, UTD, United States of America. (2021 - 2021).
  • Urbanski, M. (Author & Presenter), Sydney Dynamics Group, Random Non--Hyperbolic Exponential Maps, Online, Sydney, Australia. (2020 - 2020).
  • Other

  • Urbanski, M. (Leader), Dynamics, Measures and Dimensions Conference, Dynamics, Measures and Dimensions, National Science Foundation; Mathematical Institute of Polish Academy of Science, Banach Center in Bedlewo, Poland, Poland. (2019 - 2019).
  • Professional Meeting Contribution

  • Urbanski, M. (Coordinator/Organizer), Ergodic theory and Related Fields, Ergodic theory and related fields, University of North Texas; Stojlov Institute of Romanian Academy of Science, Bucharest, Romania, Romania. (2019 - 2019).
  • Scholarly Meeting Contribution

  • Urbanski, M. (Author & Presenter), Meeting #1165: Fall Southeastern Sectional Meeting (formerly at the University of South Alabama) Event: Topological Dynamics and Its Applications, III, The exact value of Hausdorff dimension of escaping sets of class B of meromorphic functions, Online, the University of South Alabama, United States of America. (2021 - 2021).
  • Urbanski, M. (Author & Presenter), Dynamics of (Semi-) Group Actions, Random non-hyperbolic exponential maps, Online [University of Lodz, Poland], Poland. (2021 - 2021).

Contracts, Grants, Sponsored Research

    Grant - Research

  • Urbanski, M. (Principal), "Random and Conformal Dynamical Systems [Simons]," sponsored by UNT, Private, $42000 Funded. (2018 - 2025).
  • Urbanski, M. (Principal), "Open Dynamical Systems-Singular Perturbations Approach [Simons for Sabbatical]," sponsored by UNT, Private, $114998 Funded. (2022 - 2023).
  • Urbanski, M. (Co-Principal), Chousionis, V. (Principal), Haydn, N. (Co-Principal), Pilgrim, K. (Co-Principal), "Dynamics, Measures, and Dimensions [NSF]," sponsored by University of Connecticut, Federal, $25000 Funded. (2019 - 2020).
  • Urbanski, M. (Principal), "Thermodynamic Formalism, Measures and Dimensions [NSF]," sponsored by UNT, Federal, $210000 Funded. (2014 - 2018).
  • Urbanski, M. (Co-Principal), Gao, S. (Principal), , D. (Co-Principal), Jackson, S.C. (Co-Principal), "Research Training Group in Logic and Dynamics [NSF]," sponsored by UNT, Federal, $1500000 Funded. (2010 - 2016).
  • Urbanski, M. (Principal), "Thermodynamic Formalism, Dynamics and Dimensions," sponsored by UNT, Federal, $240000 Funded. (2010 - 2014).
  • Urbanski, M. (Co-Principal), Mauldin, D. (Principal), "Measures, Dimension and Dynamics," sponsored by UNT, Federal, $280088 Funded. (2007 - 2011).
  • Urbanski, M. (Co-Principal), Mauldin, D. (Principal), "Measures, Dimension and Dynamics," sponsored by UNT, Federal, $145874 Funded. (2004 - 2008).
  • Urbanski, M. (Principal), "U.S.-Polish Collaborative Research: Ergodic Theory and Geometry of Transcendental Entire and Meromorphic Functions," sponsored by UNT, Federal, $38073 Funded. (2003 - 2008).
  • Urbanski, M. (Co-Principal), Mauldin, D. (Principal), "Measures, Dimensions and Dynamics," sponsored by UNT, Federal, $163109.00 Funded. (2001 - 2004).
  • Urbanski, M. (Co-Principal), Mauldin, D. (Principal), "Measures, Dynamics and Dimensions," sponsored by UNT, Federal, $196973.00 Funded. (1998 - 2001).
  • Urbanski, M. (Co-Principal), Mauldin, D. (Principal), "Rigidity structure of conformal dynamical systems," sponsored by UNT, State, $66310 Funded. (1996 - 1998).
  • Urbanski, M. (Co-Principal), Mauldin, D. (Principal), "Measures, Dynamics and Dimensions," sponsored by UNT, Federal, $121500.00 Funded. (1995 - 1998).
  • Urbanski, M. (Co-Principal), West, B. (Principal), Mauldin, D. (Co-Principal), "Nonlinear Structure Response to Aperiodic Forces," sponsored by UNT, International, $115000 Funded. (1994 - 1996).
  • Urbanski, M. (Co-Principal), Mauldin, D. (Principal), "Measures, Dynamics and Dimensions," sponsored by UNT, Federal, $80000.00 Funded. (1993 - 1995).
  • Urbanski, M. (Principal), Schmidt, R. (Principal), "Random and Conformal Dynamical Systems," sponsored by Simons Foundation, FOND, Funded. (2018 - 2023).
  • Urbanski, M. (Co-Principal), Chousionis, V. (Principal), Haydn, N. (Co-Principal), Pilgrim, K. (Co-Principal), "Dynamics, Measures, and Dimensions [NSF]," sponsored by University of Connecticut, Federal, Funded. (2019 - 2020).
  • Urbanski, M. (Principal), "Thermodynamic Formalism, Dynamics and Dimensions," sponsored by National Science Foundation, FED, Funded. (2014 - 2018).
  • Urbanski, M. (Principal), Mauldin, R.D. (Co-Principal), Jackson, S.C. (Principal), Gao, S. (Principal), "Research Training Group in Logic and Dynamics," sponsored by National Science Foundation, FED, Funded. (2010 - 2016).
  • Urbanski, M. (Principal), "Thermodynamic Formalism, Dynamics and Dimensions," sponsored by UNT, Federal, Funded. (2010 - 2014).
  • Urbanski, M. (Co-Principal), Mauldin, D. (Principal), "Measures, Dimension and Dynamics," sponsored by UNT, Federal, Funded. (2007 - 2011).
  • Urbanski, M. (Co-Principal), Mauldin, D. (Principal), "Measures, Dimension and Dynamics," sponsored by UNT, Federal, Funded. (2004 - 2008).
  • Grant - Service

  • Urbanski, M. (Principal), Douglass, M. (Co-Principal), "Dynamical Systems II; Denton, TX, May 2009," sponsored by UNT, Federal, $30000 Funded. (2009 - 2010).
  • Urbanski, M. (Principal), Clark, A. (Co-Principal), "Dynamical Systems, Denton 2003," sponsored by UNT, Federal, $20000 Funded. (2003 - 2004).
  • Urbanski, M. (Principal), Douglass, M. (Co-Principal), "Dynamical Systems II; Denton, TX, May 2009," sponsored by UNT, Federal, Funded. (2009 - 2010).

Service

University Service

  • Member, Topology Qualifying Exam Committee. (May 2023 - May 2024).
  • Member, PhD Committee for Taylor Jones. (October 2022 - June 2023).
  • Member, Executive Committee. (May 2021 - May 2023).
  • Member, Outreach Committee. (May 2021 - May 2022).
  • Member, Topology Qualifying Exam Committee. (May 2021 - May 2022).
  • Member, PhD Committee for Christopher James. (2021 - 2021).
  • Committee Chair, Pieter Allaart Full Professor Promotion Committee. (September 15, 2021 - October 15, 2021).
  • Member, Complex Analysis Qualyfying Exam Committee. (May 2020 - May 2021).
  • Member, Dynamical Systems Search Committee. (October 2020 - March 2021).
  • Member, John Krueger Full Professor Promotion Committee. (2020 - 2020).
  • Committee Member, PhD Committee for Robin Ragland. (2020 - 2020).
  • Committee Chair, The Graduate Affairs Committee. (May 2019 - May 2020).
  • Committee Chair, The Topology Qualifying Exam Committee. (May 2019 - May 2020).
  • Member, Executive Committee. (May 15, 2018 - May 2020).
  • Member, The Strategic Planning Committee. (September 2016 - May 2020).
  • Chairperson, Steve Jackson Eminent Faculty Award Subcommittee (of EC). (December 1, 2018 - February 2020).
  • Member, The Applied PDE Search Committee. (October 15, 2018 - 2019).
  • Member, The Topology Qualifying Exam Committee. (May 15, 2018 - May 15, 2019).
  • Member, The Graduate Affairs Committee. (May 15, 2017 - May 15, 2019).
  • Committee Chair, The Topology Qualifying Exam Committee. (May 2017 - April 2018).
  • Committee Chair, The Graduate Affairs Committee. (September 2016 - May 2017).
  • Member, The Topology Qualifying Exam Committee. (September 2016 - May 2017).
  • Member, The Executive Committee. (September 2015 - May 2017).
  • Member, The Faculty Grievance Committee. (September 2014 - May 2016).
  • Committee Chair, The Topology Qualifying Exam Committee. (August 2014 - May 2015).
  • Member, The Executive Committee. (September 2012 - May 2014).
  • Member, The Graduate Affairs Committee. (September 2011 - May 2012).
  • Member, RTG Postdoc Search Committee. (January 2012 - January 2012).

Professional Service

  • Editor, Journal Editor, Journal of Fractal Geometry. Denton, Texas. (2012 - Present).
  • Reviewer, Journal Article, Several Mathematics Journals. (2023 - 2023).
  • Reviewer, Grant Proposal, OPUS, National Center of Science. (2022 - 2022).
  • Reviewer, Journal Article, Several Mathematics Journals. (January 2022 - December 2022).
  • Reviewer, Journal Article, Several Mathematical Journals. Denton, Texas. (2021 - 2021).
  • Reviewer, Book, Book to memorialize Anatole Katok. (2020 - 2020).
  • Reviewer, Grant Proposal, Funding Agency. (2020 - 2020).
  • Reviewer, Journal Article, Several Mathematics Journals. (2020 - 2020).
  • Reviewer, Grant Proposal, Funding Agency. (2019 - 2019).
  • External T&P Letter Writer, Other Mathematics Department. (2019 - 2019).
  • Reviewer, Journal Article, Several Mathematics Journals. (2019 - 2019).
  • Reviewer, Journal Article, Several Mathematics Journals. (2019 - 2019).
  • Workshop Organizer, UNT, Stojlov Mathematical Institute of Romanian Academy of Science. Bucharest, (April 2019 - November 2019).
  • Chairperson (Organizer of the Dynamics Session), American Mathematical Society. San Francisco, California. (2018 - 2018).
  • Reviewer, Journal Article, Several Mathematics Journals. (2018 - 2018).
  • Reviewer, Journal Article, Several Mathematics Journals. (2018 - 2018).
  • Chairperson (Organizer), American Mathematical Socitey. Denton, Texas. (2017 - 2018).
  • Reviewer, Grant Proposal, Funding Agency. (2017 - 2017).
  • Reviewer, Journal Article, Several Mathematics Journals. (2017 - 2017).
  • Reviewer, Journal Article, Several Mathematics Journals. (2017 - 2017).
  • Workshop Organizer (Organizer, throughout 2012, jointly with A. Bloch and L. Oversteegen, of the Dynamical Systems Section of the 49th Spring Topology and Dynamics Conference), NSF. Bowling Green, Ohio. (May 2015 - May 2015).
  • Workshop Organizer (Co-organizer of the conference with several other members of RTG), NSF, UNT. Denton, Texas. (June 2014 - June 2014).
  • Workshop Organizer (Co-organizer of the conference with several other members of RTG), UNT, NSF. Denton, Texas. (2012 - 2012).
  • Editor, Conference Proceedings, The journal Discrete & Continuous Dynamical Systems. Denton, Texas. (July 2012 - July 2012).
  • Workshop Organizer (Organizer, jointly with B. Stratmann (Uiversity of Bremen, Germany) and A. Zdunik (University of Warsaw, Poland) of the conference “Thermodynamic Formalism, Geometry and Stochastics”), German NSF. Oberwolfach, (January 2012 - January 2012).
  • Reviewer, Grant Proposal (I have reviewed grant proposals for several funding agances all over the world), Various funding agences. Denton, Texas. (2010 - 2010).
  • Workshop Organizer (Organizer (jointly with Matt Douglass. Tushar Das. Steven Muir and Bartlomiej Skorulski)), International Conference Dynamical Systems II. Denton, Texas. (May 2009 - May 2009).
  • Workshop Organizer (Conference organizer (with Alex Clark)), NSF, UNT. Denton, Texas. (May 2003 - May 2003).
  • Session Chair (Co-organizer of a session), AMS. Austin, Texas. (October 08, 1999 - October 10, 1999).
  • Workshop Organizer (Conference co-organizer), UNT, AMS. Denton, Texas. (May 19, 1998 - May 22, 1998).
  • Workshop Organizer (conference co-organizer), UNT. Denton, Texas. (April 1997 - April 1997).
  • Other (Co-Organizer), Banach Center Symposium on Ergodic Theory and Dynamical Systems. Warsaw, (1995 - 1995).