Geometry and ergodic theory on non-recurrent elliptic functions

DOI10.1007/BF02789304zbMath1092.37025WikidataQ115181063 ScholiaQ115181063MaRDI QIDQ2565901

Mariusz Urbański, Janina Kotus

Publication date: 28 September 2005

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

zbMATH Keywords

Hausdorff dimensioncomplex dynamicsconformal measureelliptic function

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (18)

Fractal measures for meromorphic functions of finite order ⋮ Porosity in Conformal Dynamical Systems ⋮ Elliptic functions with critical points eventually mapped onto infinity ⋮ Parabolic implosion and Julia-Lavaurs sets in the exponential family ⋮ Analytic families of semihyperbolic generalized polynomial-like mappings ⋮ Geometry and ergodic theory of parabolic meromorphic functions ⋮ The Hausdorff and dynamical dimensions of self-affine sponges: a dimension gap result ⋮ Conformal measures for meromorphic maps ⋮ Unnamed Item ⋮ Hausdorff Dimension of Sets of Escaping Points and Escaping Parameters for Elliptic Functions ⋮ Hausdorff dimension of the set of elliptic functions with critical values approaching infinity ⋮ Elliptic functions with critical orbits approaching infinity ⋮ Gibbs and equilibrium measures for elliptic functions ⋮ Random non-hyperbolic exponential maps ⋮ Absence of line fields and Mañé’s theorem for nonrecurrent transcendental functions ⋮ Conformal measures for non-entire functions with critical values eventually mapped onto infinity ⋮ Thermodynamic Formalism and Geometric Applications for Transcendental Meromorphic and Entire Functions ⋮ Single and double toral band Fatou components in meromorphic dynamics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hausdorff dimension of harmonic measure on the boundary of an attractive basin for a holomorphic map
• The capacity of parabolic Julia sets
• Iterates of meromorphic functions. IV: Critically finite functions
• Differentiation of integrals in \(\mathbb{R}^n\)
• Ergodic properties and Julia sets of Weierstrass elliptic functions
• On Sullivan's conformal measures for rational maps of the Riemann sphere
• Geometric measures for parabolic rational maps
• Iterates of meromorphic functions: I
• On the Existence of Conformal Measures
• Iterates of meromorphic functions III: Preperiodic domains
• Ergodic Theory for Markov Fibred Systems and Parabolic Rational Maps
• On a theorem of Fatou
• Iteration of meromorphic functions
• Rational functions with no recurrent critical points
• Geometry and ergodic theory of conformal non-recurrent dynamics
• Iterations of holomorphic Collet-Eckmann maps: conformal and invariant measures. Appendix: On non-renormalizable quadratic polynomials
• HAUSDORFF DIMENSION AND HAUSDORFF MEASURES OF JULIA SETS OF ELLIPTIC FUNCTIONS
• Non-recurrent meromorphic functions
• Dimensions and Measures in Infinite Iterated Function Systems
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms

This page was built for publication: Geometry and ergodic theory on non-recurrent elliptic functions