Mariusz Urbanski

Department of Mathematics
University of North Texas

PAPERS

Please click on highlighted titles to download papers.

  1. "On a capacity of a continuum with non-dense orbit under a hyperbolic toral automorphism," Studia Math. 81 (1985), 37-51.
  2. "Hausdorff dimension of invariant sets for expanding maps of a circle," Ergod. Th. and Dynam. Sys. 6 (1986), 295-309.
  3. "Invariant subsets of expanding mappings of the circle," Ergod. Th. and Dynam. Sys. 7 (1987), 627-645.
  4. (With F. Przytycki), "On Hausdorff dimension of some fractal sets," Studia Math. 93 (1989), 155-186.
  5. (With F. Przytycki and A. Zdunik), "Harmonic, Gibbs and Hausdorff measures on repellers for holomorphic maps I," Ann. of Math. 130 (1989), 1-40.
  6. "Hausdorff dimension of invariant subsets for endormorphisms of the circle with an indifferent fixed point," J. London Math. Soc. (2) 40 (1989), 158-170.
  7. (With T. Bedford), "The box and Hausdorff dimension of self-affine sets," Ergod. Th. and Dynam. Sys.,10 (1990), 627-644.
  8. (With M. Denker and G. Keller), "On the uniqueness of equilibrium states for piecewise monotone maps," Studia Math. 97 (1990), 27-36.
  9. "The probability distribution and Hausdorff dimension of self-affine functions," Probab. Th. Rel. Fields 84 (1990), 377-391.
  10. "The Hausdorff dimension of the graphs of continuous self-affine functions," Proc. A.M.S. 108 (1990), 921-930.
  11. (With M. Denker), "On the existence of conformal measures," Trans. A.M.S. 328 (1991), 563-587.
  12. (With M. Denker), "Ergodic theory of Equilibrium states for rational maps," Nonlinearity 4 (1991), 103-134.
  13. (With M. Denker), "Hausdorff and conformal measures on Julia sets with a rationally indifferent periodic point," J. London Math. Soc. 43 (1991), 107-118.
  14. (With M. Denker), "On absolutely continuous invariant measures for expansive rational maps with rationally indifferent periodic points," Forum Math. 3 (1991), 561-579.
  15. (With M. Denker), "On Sullivan's conformal measures for rational maps of the Riemann sphere," Nonlinearity 4 (1991), 365-384.
  16. (With M. Denker), "On Hausdorff measures on Julia sets of subexpanding rational maps," Israel J. of Math. 76 (1991) 193-214.
  17. (With F. Przytycki and A. Zdunik), "Harmonic, Gibbs and Hausdorff measures on repellers for holomorphic maps II," Studia Math., 97 (1991), 189-225.
  18. "On Hausdorff dimension of Julia set with a rationally indifferent periodic point," Studia Math. 97 (1991), 167-188.
  19. "The Hausdorff dimension of the set of points with non-dense orbit under a hyperbolic dynamical system," Nonlinearity 4 (1991), 385-397.
  20. (With M. Denker), "Geometric measures for parabolic rational maps," Ergod. Th. and Dynam. Sys. 12 (1992), 53-66.
  21. (With M. Denker), "The dichotomy of Hausdorff measures and equilibrium states for parabolic rational maps," in Proceedings of the Conference on Ergodic Theory in Gustrow (1990), Lecture Notes in Mathematics, 1514 (1992), 90-110.
  22. (With M. Denker), "The Capacity of parabolic Julia sets," Math. Zeitsch 211, (1992), 73-86.
  23. (With J. Aaronson and M. Denker), "Ergodic theory for Markov fibered systems and parabolic rational maps," Transactions of A.M.S. 337 (1993), 495-548.
  24. (With L. Zamboni), "On free actions on (lambda)-trees," Math. Proc. Cambridge Phil. Soc., 113 (1993), 535-543.
  25. (With M. Denker), "Relating Hausdorff measures and harmonic measures on parabolic Jordan curves," Journal fur die Reine und Angewandte Mathematik, 450 (1994), 181-201.
  26. (With F. Hofbauer), "Fractal properties of invariant subsets for piecewise monotonic maps on the interval," Transactions of A.M.S., 343 (1994), 659-763.
  27. (With D. Mauldin), "Jordan curves as repellors," Pacific Journal of Math., 166 (1994), 85-97.
  28. "Rational functions with no recurrent critical points," Ergod. Th. and Dynam. Sys., 14 (1994), 391-414.
  29. (With L. Zamboni), "Circle maps, measured laminations, and free group actions on -trees, Mathematische Nachrichten, 170 (1994), 277-285.
  30. (With M. Denker and Z. Nitecki), "Conformal measures and S-Unimodal maps," Dynamical Systems and Applications of WSSIA, 4 (1995), 169-215.
  31. "A new transfinite dimension for metrizable spaces, Bull. Pol. Acad. Sci., Mathematics 43 (1995), 9-18.
  32. (With A. Volberg), "A rigidity theorem in complex dynamics," in Fractal Geometry and Stochastics, Progress in Probability 37, Birkhauser Verlag (1995).
  33. (With M. Denker and F. Przytycki), "On the transfer operator for rational functions on the Riemann sphere, Ergod. Th. and Dynam. Sys 16 (1996), 255-266 .
  34. (With D. Mauldin), "Dimensions and measures in infinite iterated function systems," Proc. London Math. Soc. (3) 73 (1996), 105-154.
  35. (With B. Stratmann), "The box-counting dimension for geometrically finite Kleinian groups," Fundamenta Mathematica 149 (1996), 83-94.
  36. "Parabolic Cantor sets," Fund. Math. 151 (1996), 241-277.
  37. "Geometry and ergodic theory of conformal nonrecurrent dynamics," Ergod. Th. and Dynam. Sys. 17 (1997), 1449-1476.
  38. (With M. Denker, D. Mauldin, and Z. Nitecki), "Conformal measures for rational functions revisited," Fundamenta Math. 157 (1998), 161-173.
  39. (With P. Hanus), "Rigidity of infinite iterated function systems," Real Anal. Exch., 24 (1998/9), 275-288.
  40. (With P. Hanus), "Complex continued fractions with restricted entries" Electronic J. Differential Equations, Vol. 8 (1998), No. 27, 1-9.
  41. (With D. Mauldin), "Dimension and measures for a curvilinear Sierpinski gasket or Apollonian packings," Adv. Math., 136 (1998), 26-38
  42. (With D. Mauldin), "On the uniqueness of the density of the invariant measure in an infinite hyperbolic iterated function system," Periodica Math. Hung. ,37 (1998), 47-53.
  43. "Hausdorff measures versus equilibrium states of conformal infinite iterated function systems", Periodica Math. Hung., 37 (1998), 153-205.
  44. (With P. Hanus), "A new class of positive recurrent functions", Contemporary Mathematics Series of AMS, 246 (1999), 123-136.
  45. (With D. Mauldin), "Conformal iterated function systems with applications to the geometry of continued fractions," Trans. of A.M.S. 351 (1999), 4995-5025.
  46. (with F. Przytycki) "Rigidity of tame rational functions," Bull. Pol. Acad. Sci. Math., 47.2 (1999), 163-182.
  47. (With D. Mauldin), "Parabolic iterated function systems," Ergod. Th. & Dynam. Sys. 20 (2000), 1423-1447.
  48. (With A. Fisher), " On invariant line fields," Bull. London Math. Soc. 32 (2000), 555-570.
  49. (With B. Stratmann), "The geometry of conformal measures for parabolic rational maps," Math. Proc. Cambridge Phil. Soc. 128 (2000), 141-156.
  50. (With B. Stratmann and M. Zinsmeister), "Well-approximable points for Julia sets with parabolic and critical points," Comp. Meth. and Funct. Th. 1 (2001), 89-97.
  51. (with F. Przytycki) "Porosity of Julia sets of non-recurrent and parabolic Collet-Eckmann rational functions," Ann. Acad. Fenn. 26 (2001), 125-154.
  52. "Porosity in conformal infinite iterated function systems" J. Number Th. 88 No. 2 (2001), 283-312
  53. (With K. Simon and B. Solomyak), "Hausdorff dimension of limit sets for parabolic IFS with overlaps," Pacific J. Math. 201 (2001), 441-478.
  54. (With K. Simon and B. Solomyak), " Invariant measures for parabolic IFS with overlaps and random continued fractions", Trans. Amer. Math. Soc. 353 (2001), 5145-5164.
  55. (With M. Zinsmeister) " Continuity of Hausdorff dimension of Julia-Lavaurs sets as a function of the phase" J. of Conformal Geometry and Dynamics, 5 (2001), 140-152..
  56. (With D. Mauldin), "Gibbs states on the symbolic space over an infinite alphabet," Israel J. of Math. 125 (2001), 93-130.
  57. (With D. Mauldin and F. Przytycki), "Rigidity of conformal iterated function systems", Compositio Math. 129 (2001), 273-299.
  58. "Rigidity of multidimensional conformal iterated function systems" Nonlinearity 14 (2001), 1593-1610.
  59. (With D. Mauldin and V. Mayer), "Rigidity of connected limit sets of conformal IFS," Michigan Math. J. 49 (2001), 451-458.
  60. (With M. Zinsmeister) "Geometry of hyperbolic Julia-Lavaurs sets" Indagationes Math. 12 (2001), 273-292
  61. (With B. Solomyak), "$L^q$ densities for measures associated with parabolic IFS with overlaps", Indiana J. Math. 50 (2001), 1845-1866.
  62. (With P. Hanus and D. Mauldin), " Thermodynamic formalism and multifractal analysis of conformal infinite iterated function systems ", Acta Math. Hungarica, 96 (2002), 27-98.
  63. (With S. Heinemann) " Hausdorff dimension estimates for infinite conformal iterated function systems ", Nonlinearity 15 (2002), 727-734.
  64. (With D. Mauldin), "Fractal measures for parabolic IFS," Advances in Math. 168 (2002), 225-253.
  65. (With B. Stratmann), "Jarnik and Julia; a Diophantine analysis for parabolic rational maps," Math. Scan. 91 (2002), 27-54.
  66. (With A. Zdunik) "Hausdorff dimensionf of harmonic measure for self-conformal sets, " Advances in Math. 171 (2002), 1-58.
  67. "The Diophantine analysis of conformal iterated function systems" Monatshefte fur Math. 137 (2002), 325-340.
  68. (With J. Kotus) " Conformal, geometric and invariant measures for transcendental expanding functions; Math. Annalen 324 (2002), 619-656.
  69. (With T. Bedford and A. Fisher), "The scenery flow for hyperbolic Julia sets," Proc. London Math. Soc. 85 (2002), 467-492.
  70. (With J. Kotus) "Existence of invariant measures for transcendental subexpanding functions"; Math. Zeitschrift 243 (2003), 25-36.
  71. (With J. Kotus) " Hausdorff dimension and Hausdorff measures of Julia sets of elliptic functions, Bull. London Math. Soc. 35 (2003), 269-275,
  72. (With E. Mihailescu) " Holomorphic maps for which unstable manifolds depend on prehistories, Discrete & Continuous Dynam. Sys. 9 (2003), 443-450.
  73. (With F. Gonzales and O. Jenkinson) " On transfer operator of continued fractions with restricted entries, Proc. London Math. Soc. 86 (2003), 755-778.
  74. " Thermodynamic formalism, topological pressure and escape rates for non-recurrent conformal dynamics" Fund. Math. 176 (2003), 97-125.
  75. " Measures and dimensions in conformal dynamics" Bull. Amer. Math. Soc. 40 (2003), 281-321.
  76. (With A. Zdunik) " The finer geometry and dynamics of exponential family" Michigan Math. J. 51 (2003), 227-250.
  77. (With D. Mauldin) " The doubling property of conformal measures of infinite iterated function systems" J. Number Th. 102 (2003), 23-40.
  78. " Optimal periodic orbits for non-recurrent rational functions, Math. Bull. Pol. Acad. Sci. 51 (2003), 175-184.
  79. (With V. Mayer), "Finer Geometric Rigidity of limit sets of conformal IFS," Proc. Amer. Math. Soc. 131 (2003), 3605-3702.
  80. (With B. Stratmann), " Real Analyticity of Topological Pressure for parabolically semihyperbolic generalized polynomial-like maps, Indag. Mathem. 14 (2003), 119-134.,".
  81. (With V. Maume Deschamp, B. Schmitt and A. Zdunik) " Pressure and recurrence, Fund. Math. 178 (2003), 129-141.
  82. (With M. Roy), " Conformal families of measures for fibred systems, " Monatshefte fur Mathematik 140 (2003), 135-145.
  83. (With A. Zdunik), "Real analyticity of Hausdorff dimension of finer Julia sets of exponential family", Ergod Th. and Dynam. Sys. 24 (2004), 279-315.
  84. (With B. Stratmann), "Multifractal analysis for parabolically semihyperbolic generalized polynomial-like maps", IP New Studies in Advanced Mathematics, 5 (2004), 393-347.
  85. (With E. Mihailescu) " Inverse topological pressure with applications to holomorphic dynamics of several complex variables ", Comm. in Contemporary Math. 6 (2004), 653-681.
  86. (With A. Zdunik) " The parabolic map ${1\over e}e^z$ ", Indagationes Math. 15 (2004), 419-433.
  87. (With B. Stratmann), "Metrical Diophantine analysis for tame parabolic iterated function systems," Pacific J. Math. 216 (2004), 361-392.
  88. (With J. Kotus) " Geometry and ergodic theory of non-recurrent elliptic functions; " J. d'Analyse Math. 93 (2004), 35-102.
  89. (With C. Wolf), " SRB measures for Axiom A endomorphisms ", Math. Research Letters, 11 (2004), 785-797.
  90. " Finer diophantine and regularity properties of $1$-dimensional parabolic IFS, " Preprint 2005, to appear Real Analysis Exch.
  91. " Thermodynamic Formalism and Multifractal Analysis of Finer Julia Sets of Exponential Family ", , Preprint 2005.
  92. " Diophantine approximation of self-conformal measures, J. Number Th. 110 (2005), 219-235.
  93. (With J. Kotus) "The dynamics and geometry of the Fatou functions", Discrete and Continuous Dynam. Sys., 13 (2005), 291-338
  94. (With V. Mayer), " Gibbs and equilibrium measures for elliptic functions", Math. Zeit. 250 (2005), 657-683.
  95. (With E. Mihailescu) " Estimates for the stable dimension for holomorphic maps", Houston J. Math. 31 (2005), 367-389.
  96. (With O. Jenkinson and D. Mauldin) " Zero temperature limits of Gibbs-equilibrium states for countable alphabet subshifts of finite type", J. Statistical Physics 119 (2005), 765-776.
  97. (With V. Mayer), " Exponential elliptics give dimension two", Illinois J. Math. 49 (2005), 291-294.
  98. " Diophantine approximation of conformal measures of one-dimensional iterated function systems, Compositio Math. 141 (2005) 869-886.
  99. (With M. Roy), " Regularity properties of Hausdorff dimension in infinite IFS, Ergod. Th. and Dynam. Sys. 25 (2005), 1961-1983.
  100. (With B. Stratmann), " Diophantine extremality of the Patterson measure", Math. Proc. Cambridge Phil. Soc. 140 (2006), 297-304.
  101. (With B. Karpinska), " How points escape to infinity under exponential maps, " Journal London Math. Soc. 73 (2006), 141-156.
  102. (With J. Kotus) " Geometric rigidity of transcendental meromorphic functions ", Math. Zeit. 253 (2006), 227-233.
  103. (With J. Kotus) " Virtual Centers of Hyperbolic Components in the Tangent Family; Hausdorff Dimension Outlook ", Ergod. Th. and Dynam. Sys. 26 (2006), 769-782.
  104. " Analytic Families of Semihyperbolic Generalized Polynomial-Like Mappings, ", Preprint 2006, to appear Monatshefte fur Math.
  105. (With V. Mayer), " Thermodynamical Formalism and Multifractal Analysis for Meromorphic Functions of Finite Order ", Preprint 2006, to appear Memoirs of AMS
  106. (With A. Bis) " Some remarks on topological entropy of a semigroup of continuous maps, Cubo J. 8 (2006), 63-71.
  107. (With J. Kotus) " Geometry and dynamics of some meromorphic functions, Mathem. Nachr. 279 (2006), 1565-1584.
  108. (With O. Jenkinson and D. Mauldin) " Ergodic optimization for countable alphabet subshifts of finite type, Ergod. Th. and Dynam. Sys. 26 (2006), 1791-1803.
  109. (With M. Zinsmeister) "Parabolic implosion and Julia-Lavaurs sets in the exponential family", Monatsh. Math. 149 (2006), 129-140.
  110. (With A. M. Davie and A. Zdunik), " Maximizing measures on Metrizable Non-Compact Spaces ", Proc. Edinburgh Math. Soc. 50 (2007), 123-151.
  111. (With A. Zdunik) " Geometry and ergodic theory of non-hyperbolic exponential maps ", Trans. AMS 359 (2007), 3973-3997.
  112. " Recurrence rates for loosely Markov dynamical systems, J. Australian Math. Soc. 82 (2007), 39-57.
  113. (With V. Mayer), " Fractal measures for meromorphic functions of finite order ", Dyn. Sys. 22 (2007), 169-178.
  114. (With J. Kotus) " The class of pseudo non-recurrent elliptic functions; geometry and dynamics, " Preprint 2007. ,
  115. (With H. Sumi) " Real analyticity of Hausdorff dimension for expanding rational semigroups, " Preprint 2007. to appear Ergod. Th. & Dynam. Sys.
  116. (With J. Kotus) " Hausdorff dimension of radial and escaping points for transcendental meromorphic functions, " Preprint 2007, to appear Illinois J. Math.
  117. (With B. Stratmann), " Pseudo-Markov systems and infinitely generated Schottky groups", Amer. J. Math. 129 (2007), 1019-1062
  118. (With M. Kesseboehmer) " Higher-Dimensional Multifractal Value Sets for Conformal Infinite Graph Directed Markov Systems, " Nonlinearity 20 (2007), 1969-1985.
  119. (With O. Jenkinson and D. Mauldin) " Ergodic optimization for non-compact dynamical systems", Dynamical Systems 22 (2007), 379-388.
  120. (With V. Mayer), " Ergodic properties of sub-hyperbolic functions with polynomial Schwarzian derivative ", Preprint 2007, to appear Proc. Edinburgh Math. Soc.
  121. (With A. Zdunik) " Instability of exponential Collet - Eckmann maps", Israel J. Math. 161 (2007), 347 - 371.
  122. (With E. Mihailescu) " Inverse pressure estimates and the independence of stable dimension for non-invertible maps ", Canadian. J. Math. 60 (2008), 658-684.
  123. (With E. Mihailescu) " Transversal Families of Skew-Product Axiom A Endomorphisms ", Discrete and Continuous Dynamical Systems 21 (2008), 907-928.
  124. (With M. Roy), " Real Analyticity of Hausdorff Dimension for Higher Dimensional Graph Directed Markov Systems ", Mathematische Zeitschrift 260 (2008), 153-175
  125. (With A. Bis) " Geometry of Markov Systems and Codimension-One Foliations, ", Ann. Polon. Math. 94 (2008), 187-196.
  126. (With V. Mayer and B. Skorulski), " Random Distance Expanding Mappings, Thermodynamic Formalism, Gibbs Measures, and Fractal Geometry ", Preprint 2008
  127. " Geometric Rigidity for the Class S of Transcendental Meromorphic Functions ", Preprint 2008, to appear Proc. AMS
  128. " Transfinite Hausdorff Dimension ", Preprint 2008, to appear Topology and its Applications.
  129. (with M. Roy) " Mulitifractal Analysis for Conformal Graph Directed Markov Systems ", Preprint 2008, to appear Discrete & Continuous Dynam. Sys.
  130. (with R. D. Mauldin and T. Szarek) " Graph Directed Markov Systems on Hilbert Spaces ", Preprint 2008, to appear Math. Proc. Cambridge Phil. Soc.
  131. (With J. Kotus) " Fractal measures and ergodic theory of transcendental meromorphic functions (research expository article) ", London Math. Soc. Lect. Notes. 348 (2008), Volume: Transcendental Dynamics and Complex Analysis.
  132. (With E. Mihailescu) " Relations between Stable Dimension and the Preimage Counting Function on Basic Sets with Overlaps ", Preprint 2008. To appear Bull. London Math. Soc.
  133. (With G. Havard and M. Zinsmeister) " Variation in Hausdorff Dimension in the exponential family, ", Preprint 2008.
  134. (With V. Mayer), " Geometric thermodynamical formalism and real analyticity for meromorphic functions of finite order ", Ergod. Theory & Dynam. Sys., 28 (2008), 915 - 946.
  135. (With M. Roy and H. Sumi), " Analytic Families of Holomorphic IFS ", Nonlinearity, 21 (2008), 2255-2279.
  136. (With H. Sumi) " Measures and Dimensions of Julia sets of Semi-hyperbolic Rational Semigroups ", Preprint 2008.
  137. (With T. Das) " The Geometry of Baire Spaces ", Preprint 2008.
  138. (With C. Wolf), " Ergodic Theory of Parabolic Horseshoes", Comm. Math. Phys. 281 (2008), 711-751.
  139. (With A. Zdunik) " Ergodic Theory for Holomorphic Endomorphisms of Complex Projective spaces ", Preprint 2009.
  140. (With H. Akter) " Real Analyticity of Hausdorff Dimension of Julia Sets of Parabolic Polynomials f_\lambda(z)=z(1-z-\lamda z^{2})}", Preprint 2009.
  141. (With T. Szarek and M. Sleczka) " On Stability of Velocity Vectors for Some Passive Tracer Models ", Preprint 2009.
  142. (With M. Roy and H. Sumi), " $\lambda$ topology vs. pointwise topology, ", Ergod. Th. & Dynam. Sys. 29 (2009), 685-713.
  143. (With H. Sumi) " The Equilibrium States for Semigroups of Rational Functions, ", Monatshefte fur Math. 156 (2009), 371-390.

Mariusz Urbanski
urbanski@unt.edu   (940)565-3323   Return to my homepage
Revised 04/26/2009