Conformal, geometric and invariant measures for transcendental expanding functions

DOI10.1007/s00208-002-0356-yzbMath1009.37032OpenAlexW2059578144WikidataQ115181067 ScholiaQ115181067MaRDI QIDQ1865573

Mariusz Urbański, Janina Kotus

Publication date: 27 March 2003

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-002-0356-y

zbMATH Keywords

Julia setHausdorff dimensionconformal mapsfractal structureexpanding maps

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems (37F15) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50)

Related Items (14)

Bowen’s formula for meromorphic functions ⋮ Fractal measures for meromorphic functions of finite order ⋮ Gibbs state for some class of meromorphic functions ⋮ Geometry and ergodic theory of parabolic meromorphic functions ⋮ Geometric thermodynamic formalism and real analyticity for meromorphic functions of finite order ⋮ Conformal measures for meromorphic maps ⋮ Thermodynamic formalism and integral means spectrum of logarithmic tracts for transcendental entire functions ⋮ On conformal measures of parabolic meromorphic functions ⋮ Dynamics of hyperbolic meromorphic functions ⋮ Thermodynamic formalism of transcendental entire maps of finite singular type ⋮ Geometric rigidity of transcendental meromorphic 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 ⋮ Finer fractal geometry for analytic families of conformal dynamical systems

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