Faculty Profile

Mariusz Urbanski

Title
Professor
Department
Mathematics
College
College of Science

    

Education

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

Current Scheduled Teaching*

MATH 6950.719, Doctoral Dissertation, Spring 2023
MATH 6950.711, Doctoral Dissertation, Fall 2022

* Texas Education Code 51.974 (HB 2504) requires each institution of higher education to make available to the public, a syllabus for undergraduate lecture courses offered for credit by the institution.

Previous Scheduled Teaching*

MATH 6950.714, Doctoral Dissertation, Spring 2022
MATH 4500.001, Introduction to Topology, Spring 2022 Syllabus SPOT
MATH 5600.001, Introduction to Topology, Spring 2022 SPOT
MATH 5900.703, Special Problems, Spring 2022
MATH 6950.710, Doctoral Dissertation, Fall 2021
MATH 3610.001, Real Analysis II, Fall 2021 Syllabus SPOT
MATH 6200.001, Topics in Ergodic Theory, Fall 2021 Syllabus SPOT
MATH 6950.723, Doctoral Dissertation, Spring 2021
MATH 6910.702, Special Problems, Spring 2021
MATH 5620.001, Topology, Spring 2021 Syllabus SPOT
MATH 5620.002, Topology, Spring 2021 Syllabus SPOT
MATH 5620.601, Topology, Spring 2021 Syllabus SPOT
MATH 3410.004, Differential Equations I, Fall 2020 Syllabus SPOT
MATH 6950.723, Doctoral Dissertation, Fall 2020
MATH 5310.001, Real Analysis, Fall 2020 Syllabus SPOT
MATH 5310.011, Real Analysis, Fall 2020
MATH 5310.601, Real Analysis, Fall 2020 Syllabus SPOT
MATH 6900.723, Special Problems, Fall 2020
MATH 6900.724, Special Problems, Fall 2020
MATH 3410.006, Differential Equations I, Spring 2020 Syllabus
MATH 6950.723, Doctoral Dissertation, Spring 2020
MATH 3000.001, Real Analysis I, Spring 2020 Syllabus
MATH 6900.703, Special Problems, Spring 2020
MATH 6950.704, Doctoral Dissertation, Fall 2019
MATH 3610.001, Real Analysis II, Fall 2019 Syllabus SPOT
MATH 5900.723, Special Problems, Fall 2019
MATH 6900.723, Special Problems, Fall 2019
MATH 6200.001, Topics in Ergodic Theory, Fall 2019 SPOT
MATH 6950.725, Doctoral Dissertation, Spring 2019
MATH 3000.001, Real Analysis I, Spring 2019 Syllabus SPOT
MATH 5900.707, Special Problems, Spring 2019
MATH 6900.704, Special Problems, Spring 2019
MATH 3410.008, Differential Equations I, Fall 2018 Syllabus SPOT
MATH 6950.723, Doctoral Dissertation, Fall 2018
MATH 6150.001, Functional Analysis, Fall 2018 SPOT
MATH 6950.705, Doctoral Dissertation, Summer 5W1 2018
MATH 6950.725, Doctoral Dissertation, Spring 2018
MATH 6200.001, Topics in Ergodic Theory, Spring 2018 SPOT
MATH 6950.704, Doctoral Dissertation, Fall 2017
MATH 6950.709, Doctoral Dissertation, Fall 2017
MATH 6950.723, Doctoral Dissertation, Fall 2017
MATH 5310.001, Functions of a Real Variable, Fall 2017 SPOT
MATH 6950.725, Doctoral Dissertation, Spring 2017
MATH 6900.725, Special Problems, Spring 2017
MATH 6900.726, Special Problems, Spring 2017
MATH 5620.001, Topology, Spring 2017 SPOT
MATH 6950.723, Doctoral Dissertation, Fall 2016
MATH 6210.001, Dynamical Systems Seminar, Fall 2016
MATH 6900.723, Special Problems, Fall 2016
MATH 5610.001, Topology., Fall 2016 SPOT
MATH 6950.725, Doctoral Dissertation, Spring 2016
MATH 6950.722, Doctoral Dissertation, Fall 2015
MATH 6210.001, Dynamical Systems Seminar, Fall 2015
MATH 5900.723, Special Problems, Fall 2015
MATH 6610.001, Topics in Topology and Geometry, Fall 2015 SPOT
MATH 5900.725, Special Problems, Spring 2015
MATH 6900.725, Special Problems, Spring 2015
MATH 6200.001, Topics in Ergodic Theory, Spring 2015
MATH 5900.711, Special Problems, Fall 2014
MATH 6900.722, Special Problems, Fall 2014
MATH 6200.001, Topics in Ergodic Theory, Fall 2014
MATH 5910.701, Special Problems, Summer 10W 2014
MATH 6220.001, Logic and Dynamics Seminar, Spring 2014
MATH 5900.725, Special Problems, Spring 2014
MATH 5910.725, Special Problems, Spring 2014
MATH 6900.725, Special Problems, Spring 2014
MATH 5620.001, Topology, Spring 2014
MATH 6220.001, Logic and Dynamics Seminar, Fall 2013
MATH 4900.702, Special Problems, Fall 2013
MATH 5900.711, Special Problems, Fall 2013
MATH 5610.001, Topology., Fall 2013
MATH 5900.723, Special Problems, Spring 2013
MATH 6200.001, Topics in Ergodic Theory, Spring 2013
MATH 5900.711, Special Problems, Fall 2012
MATH 6200.001, Topics in Ergodic Theory, Fall 2012
MATH 6950.702, Doctoral Dissertation, Summer 10W 2012
MATH 6950.707, Doctoral Dissertation, Spring 2012
MATH 6900.702, Special Problems, Spring 2012
MATH 5620.001, Topology, Spring 2012
MATH 6950.722, Doctoral Dissertation, Fall 2011
MATH 2700.001, Linear Algebra and Vector Geometry, Fall 2011 Syllabus
MATH 6900.702, Special Problems, Fall 2011
MATH 5610.001, Topology., Fall 2011
MATH 6950.722, Doctoral Dissertation, Summer 5W2 2011
MATH 5450.001, Calculus on Manifolds, Spring 2011
MATH 6950.707, Doctoral Dissertation, Spring 2011
MATH 6900.702, Special Problems, Spring 2011
MATH 6950.722, Doctoral Dissertation, Fall 2010
MATH 2700.004, Linear Algebra and Vector Geometry, Fall 2010 Syllabus
MATH 6900.702, Special Problems, Fall 2010
MATH 6110.001, Topics in Analysis, Fall 2010
MATH 6950.720, Doctoral Dissertation, Spring 2010
MATH 6900.720, Special Problems, Spring 2010
MATH 6200.001, Topics in Ergodic Theory, Spring 2010
MATH 6950.722, Doctoral Dissertation, Fall 2009
MATH 6900.702, Special Problems, Fall 2009
MATH 6910.722, Special Problems, Fall 2009
MATH 6200.001, Topics in Ergodic Theory, Fall 2009
MATH 3740.001, Vector Calculus, Fall 2009 Syllabus
MATH 6950.720, Doctoral Dissertation, Spring 2009
MATH 4500.001, Introduction to Topology, Spring 2009 Syllabus
MATH 5600.001, Introduction to Topology, Spring 2009
MATH 6900.720, Special Problems, Spring 2009
MATH 6900.772, Special Problems, Spring 2009
MATH 6910.720, Special Problems, Spring 2009
MATH 6110.002, Topics in Analysis, Spring 2009
MATH 6950.722, Doctoral Dissertation, Fall 2008
MATH 6900.702, Special Problems, Fall 2008
MATH 6110.001, Topics in Analysis, Fall 2008
MATH 6950.720, Doctoral Dissertation, Spring 2008
MATH 6950.722, Doctoral Dissertation, Fall 2007
MATH 5900.772, Special Problems, Fall 2007
MATH 6900.702, Special Problems, Fall 2007
MATH 6200.003, Topics in Ergodic Theory, Fall 2007
MATH 6950.720, Doctoral Dissertation, Spring 2007
MATH 5900.752, Special Problems, Spring 2007
MATH 6900.720, Special Problems, Spring 2007
MATH 6900.772, Special Problems, Spring 2007
MATH 6200.001, Topics in Ergodic Theory, Spring 2007
MATH 6950.722, Doctoral Dissertation, Fall 2006
MATH 2510.001, Real Analysis I, Fall 2006
MATH 6900.702, Special Problems, Fall 2006
MATH 6200.001, Topics in Ergodic Theory, Fall 2006
MATH 6900.700, Special Problems, Summer 3W1 2006
MATH 6900.722, Special Problems, Summer 5W2 2006
MATH 6910.772, Special Problems, Summer 5W2 2006
MATH 6950.720, Doctoral Dissertation, Spring 2006
MATH 5900.723, Special Problems, Spring 2006
MATH 6900.720, Special Problems, Spring 2006
MATH 6110.001, Topics in Analysis, Spring 2006
MATH 1100.024, College Algebra, Fall 2005
MATH 6950.722, Doctoral Dissertation, Fall 2005
MATH 6940.703, Individual Research, Fall 2005
MATH 6900.702, Special Problems, Fall 2005
MATH 5200.003, Topics in Dynamical Systems, Fall 2005
MATH 6950.720, Doctoral Dissertation, Spring 2005
MATH 5950.720, Master's Thesis, Spring 2005
MATH 2520.002, Real Analysis II, Spring 2005
MATH 6900.720, Special Problems, Spring 2005
MATH 6950.722, Doctoral Dissertation, Fall 2004
MATH 2510.001, Real Analysis I, Fall 2004
MATH 6900.702, Special Problems, Fall 2004
MATH 3740.001, Vector Calculus, Fall 2004

* Texas Education Code 51.974 (HB 2504) requires each institution of higher education to make available to the public, a syllabus for undergraduate lecture courses offered for credit by the institution.

Published Publications

Published Intellectual Contributions

Abstracts and Proceedings
Urbanski, M. (2003). On transfer operator of continued fractions with restricted entries.
Urbanski, M. (1996). Dimensions and measures in innite iterated function systems.
Book
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.
Urbanski, M., Przytycki, F. (2010). Conformal Fractals: Ergodic Theory Methods. Cambridge University Press; The London Mathematical Society.
Urbanski, M. (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.
Urbanski, M. (1995). A rigidity theorem in complex dynamics, in Fractal Geometry andStochastics. Progress in Probability 37, Birkhauser Verlag (1995).
Urbanski, M. (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
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., 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.
Urbanski, M. (2010). Ergodic properties of sub-hyperbolic functions with polynomial Schwarzian derivative.
Urbanski, M. (2010). On Stability of Velocity Vectors for Some Passive Tracer Models,.
Urbanski, M. (2010). Real Analyticity of Hausdorff Dimension for Expanding Rational Semigroups.
Urbanski, M. (2010). Relations between stable dimension and the preimage counting function on basic sets with overlaps.
Urbanski, M. (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.
Urbanski, M. (2009). Graph Directed Markov Systems on Hilbert Spaces.
Urbanski, M. (2009). Lambda-topology vs. pointwise topology.
Urbanski, M. (2009). Multifractal analysis for conformal graph directed Markov systems.
Urbanski, M. (2009). The Equilibrium States for Semigroups of Rational Maps, Monatshefte fur Math. 156 (2009), 371-390.
Urbanski, M. (2009). Transfinite Hausdorff Dimension.
Urbanski, M. (2008). Analytic Families of Holomorphic IFS.
Urbanski, M. (2008). Ergodic Theory of Parabolic Horseshoes.
Urbanski, M. (2008). Fractal Measures and Ergodic Theory of Transcendental Meromorphic Functions.
Urbanski, M. (2008). Geometric Thermodynamical Formalism and Real Analyticity for Meromorphic Functions of Finite Order.
Urbanski, M. (2008). Geometry of Markov Systems and Codimension-One Foliations.
Urbanski, M. (2008). Hausdorff dimension of radial and escaping points for transcendental meromorphic functions.
Urbanski, M. (2008). Inverse pressure estimates and the independence of stable dimension for non-invertible maps.
Urbanski, M. (2008). Real Analyticity of Hausdorff Dimension for Higher Dimensional Graph Directed Markov Systems.
Urbanski, M. (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.
Urbanski, M. (2007). Fractal Measures for Meromorphic Functions of Finite Order.
Urbanski, M. (2007). Geometry and ergodic theory of non-hyperbolic exponential maps.
Urbanski, M. (2007). Higher-Dimensional Multifractal Value Sets for Infinite Graph Directed Markov Systems.
Urbanski, M. (2007). Instability of Exponential Collet - Eckmann Maps.
Urbanski, M. (2007). Maximizing Measures on Metrizable Non-Compact Spaces.
Urbanski, M. (2007). Pseudo-Markov Systems and Infinitely Generated Schottky Groups.
Urbanski, M. (2007). Recurrence Rates for Loosely Markov Dynamical Systems.
Urbanski, M. (2006). Diophantine Extremality of the Patterson Measure.
Urbanski, M. (2006). Ergodic optimization for countable alphabet subshifts of infinite type.
Urbanski, M. (2006). Finer Diophantine and regularity properties of 1-Dimensional Parabolic IFS.
Urbanski, M. (2006). Geometric rigidity of transcendental meromorphic functions.
Urbanski, M. (2006). Geometry and dynamics of some meromorphic functions.
Urbanski, M. (2006). How points escape to innity under exponential maps.
Urbanski, M. (2006). Parabolic Implosion and Julia-Lavaurs Sets in the ExponentialFamily.
Urbanski, M. (2006). Some remarks on topological entropy of a semigroup of countinuous maps.
Urbanski, M. (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.
Urbanski, M. (2005). Exponential elliptics give dimension two.
Mayer, V., Urbanski, M. (2005). Exponential elliptics give dimension two. Illinois Journal of Mathematics. 49(1), 291-294.
Urbanski, M. (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.
Urbanski, M. (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.
Urbanski, M. (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.
Urbanski, M. (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.
Urbanski, M. (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.
Urbanski, M. (2003). Finer Geometric Rigidity of Limit Sets of Conformal IFS. Proceedings of the American Mathematical Society. 131, 3695‑3702.
Mayer, V., Urbanski, M. (2003). Finer geometric rigidity of limit sets of conformal IFS. Proceedings of the American Mathematical Society. 131(12), 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.
Urbanski, M. (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.
Urbanski, M. (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.
Urbanski, M. (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.
Urbanski, M. (2001). V. Mayer Rigidity of connected limit sets of conformal IFS.
Urbanski, M. (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.
Mauldin, R., Urbanski, M. (2000). Parabolic iterated function systems. Ergodic Theory and Dynamical Systems. 20, 1423-1447.
Urbanski, M. (2000). Parabolic iterated function systems.
Stratmann, B., Urbanski, M. (2000). The geometry of conformal measures for parabolic rational maps. Mathematical Proceedings of the Cambridge Philosophical Society. 128, 141-156.
Urbanski, M. (2000). The geometry of conformal measures for parabolic rationalmaps. Mathematical Proceedings of the Cambridge Philosophical Society.
Urbanski, M. (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.
Urbanski, M. (1999). Rigidity of tame rational functions.
Urbanski, M. (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.
Urbanski, M. (1998). On the uniqueness of the density for the invariant measure in aninfinite hyperbolic iterated function system.
Urbanski, M. (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.
Urbanski, M. (1995). Conformal measures and S-Unimodal maps.
Urbanski, M. (1994). Circle Maps, Measured Laminations, and Free Group Actions onIR- Trees.
Urbanski, M. (1994). Fractal properties of invariant subsets for piecewise monotonicmaps on the interval.
Urbanski, M. (1994). Jordan curves as repellors.
Urbanski, M. (1994). Rational functions with no recurrent critical points.
Urbanski, M. (1994). Relating Hausdor measures and harmonic measures on parabolicJordan curves.
Urbanski, M. (1993). Ergodic theory for Markov bered systems and parabolic rational maps.
Urbanski, M. (1993). On free actions on -trees. Mathematical Proceedings of the Cambridge Philosophical Society.
Urbanski, M. (1992). Geometric measures for parabolic rational maps.
Urbanski, M. (1992). The Capacity of parabolic Julia sets.
Urbanski, M. (1991). Ergodic theory of equilibrium states for rational maps.
Urbanski, M. (1991). Harmonic, Gibbs and Hausdorff measureson repellers for holomorphic maps II.
Urbanski, M. (1991). Hausdor and conformal measures on Julia sets with a rationallyindifferent periodic point.
Urbanski, M. (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.
Urbanski, M. (1991). On Hausdorff measures on Julia sets of subexpanding rationalmaps.
Urbanski, M. (1991). On Sullivan's conformal measures for rational maps of the Riemannsphere.
Urbanski, M. (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.
Urbanski, M. (1990). On the uniqueness of equilibrium states for piecewise monotone maps.
Urbanski, M. (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.
Urbanski, M. (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.
Urbanski, M. (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.
Urbanski, M. (2010). Thermodynamical Formalism and Multifractal Analysis for Meromorphic Functions of Finite Order. 105.

Awarded Grants

Contracts, Grants and Sponsored Research

Fellowship
Urbanski, M. (Principal), "Open Dynamical Systems-Singular Perturbations Approach," Sponsored by UNT, Private, $114999 Funded. (August 1, 2022July 31, 2023).
Grant - Research
Urbanski, M. (Principal), "Random and Conformal Dynamical Systems [Simons]," Sponsored by UNT, Private, $42000 Funded. (September 01, 2018August 31, 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. (February 01, 2019January 31, 2020).
Urbanski, M. (Principal), "Thermodynamic Formalism, Measures and Dimensions [NSF]," Sponsored by UNT, Federal, $210000 Funded. (September 01, 2014August 31, 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. (May 15, 2010April 30, 2016).
Urbanski, M. (Principal), "Thermodynamic Formalism, Dynamics and Dimensions," Sponsored by UNT, Federal, $240000 Funded. (June 01, 2010May 30, 2014).
Urbanski, M. (Co-Principal), Mauldin, D. (Principal), "Measures, Dimension and Dynamics," Sponsored by UNT, Federal, $280088 Funded. (June 01, 2007May 31, 2011).
Urbanski, M. (Co-Principal), Mauldin, D. (Principal), "Measures, Dimension and Dynamics," Sponsored by UNT, Federal, $145874 Funded. (June 01, 2004May 31, 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. (June 01, 2003May 31, 2008).
Urbanski, M. (Co-Principal), Mauldin, D. (Principal), "Measures, Dimensions and Dynamics," Sponsored by UNT, Federal, $163109.00 Funded. (June 01, 2001May 31, 2004).
Urbanski, M. (Co-Principal), Mauldin, D. (Principal), "Measures, Dynamics and Dimensions," Sponsored by UNT, Federal, $196973.00 Funded. (June 01, 1998May 31, 2001).
Urbanski, M. (Co-Principal), Mauldin, D. (Principal), "Rigidity structure of conformal dynamical systems," Sponsored by UNT, State, $66310 Funded. (19961998).
Urbanski, M. (Co-Principal), Mauldin, D. (Principal), "Measures, Dynamics and Dimensions," Sponsored by UNT, Federal, $121500.00 Funded. (June 01, 1995May 31, 1998).
Urbanski, M. (Co-Principal), West, B. (Principal), Mauldin, D. (Co-Principal), "Nonlinear Structure Response to Aperiodic Forces," Sponsored by UNT, International, $115000 Funded. (19941996).
Urbanski, M. (Co-Principal), Mauldin, D. (Principal), "Measures, Dynamics and Dimensions," Sponsored by UNT, Federal, $80000.00 Funded. (July 01, 1993June 30, 1995).
Grant - Service
Urbanski, M. (Principal), Douglass, M. (Co-Principal), "Dynamical Systems II; Denton, TX, May 2009," Sponsored by UNT, Federal, $30000 Funded. (March 01, 2009February 28, 2010).
Urbanski, M. (Principal), Clark, A. (Co-Principal), "Dynamical Systems, Denton 2003," Sponsored by UNT, Federal, $20000 Funded. (May 01, 2003April 30, 2004).
,
Overall
Summative Rating
Challenge and
Engagement Index
Response Rate

out of 5

out of 7
%
of
students responded
  • Overall Summative Rating (median):
    This rating represents the combined responses of students to the four global summative items and is presented to provide an overall index of the class’s quality. Overall summative statements include the following (response options include a Likert scale ranging from 5 = Excellent, 3 = Good, and 1= Very poor):
    • The course as a whole was
    • The course content was
    • The instructor’s contribution to the course was
    • The instructor’s effectiveness in teaching the subject matter was
  • Challenge and Engagement Index:
    This rating combines student responses to several SPOT items relating to how academically challenging students found the course to be and how engaged they were. Challenge and Engagement Index items include the following (response options include a Likert scale ranging from 7 = Much higher, 4 = Average, and 1 = Much lower):
    • Do you expect your grade in this course to be
    • The intellectual challenge presented was
    • The amount of effort you put into this course was
    • The amount of effort to succeed in this course was
    • Your involvement in course (doing assignments, attending classes, etc.) was
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