Finer fractal geometry for analytic families of conformal dynamical systems

DOI10.1080/14689367.2014.903385zbMath1350.37027OpenAlexW2048625701MaRDI QIDQ2875544

Mariusz Urbański, Bartłomiej Skorulski

Publication date: 8 August 2014

Published in: Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/14689367.2014.903385

zbMATH Keywords

Hausdorff dimensioniterated function systemsfractal geometryconformal dynamicsmeromorphic transcendental functions

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Iteration theory, iterative and composite equations (39B12) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50) Dimension theory of smooth dynamical systems (37C45)

Related Items (7)

Porosity in Conformal Dynamical Systems ⋮ Thin annuli property and exponential distribution of return times for weakly Markov systems ⋮ The failure of Ruelle's property for entire functions ⋮ Parabolic arcs of the multicorns: real-analyticity of Hausdorff dimension, and singularities of \(\mathrm{Per}_n(1)\) curves ⋮ Real analyticity for random dynamics of transcendental functions ⋮ Long hitting times for expanding systems ⋮ Thermodynamic Formalism and Geometric Applications for Transcendental Meromorphic and Entire Functions

Cites Work

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• Repellers for real analytic maps
• Dimensions and Measures in Infinite Iterated Function Systems
• Non-existence of absolutely continuous invariant probabilities for exponential maps
• Regularity properties of Hausdorff dimension in infinite conformal iterated function systems

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