Mariusz Urbanski

Previous Scheduled Teaching

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.

Contracts, Grants and 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).