Periodic points and the measure of maximal entropy of an expanding Thurston map

DOI10.1090/TRAN/6705zbMath1366.37074arXiv1311.6906OpenAlexW2962776921MaRDI QIDQ2822726

Zhi-Qiang Li

Publication date: 4 October 2016

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.6906

zbMATH Keywords

fixed pointperiodic pointmeasure of maximal entropyvisual metricexpanding Thurston mappostcritically finite map

Mathematics Subject Classification ID

Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems (37F15) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Low-dimensional topology of special (e.g., branched) coverings (57M12) Combinatorics and topology in relation with holomorphic dynamical systems (37F20)

Related Items (3)

Equilibrium states for expanding Thurston maps ⋮ Prime orbit theorems for expanding Thurston maps: Dirichlet series and orbifolds ⋮ Thermodynamic formalism for coarse expanding dynamical systems

Cites Work

• Preperiodic points and unlikely intersections
• Random matrix products and measures on projective spaces
• The thermodynamic formalism for expanding maps
• Complex dynamics
• A proof of Thurston's topological characterization of rational functions
• An invariant measure for rational maps
• Uniqueness of equilibrium measures for countable Markov shifts and multidimensional piecewise expanding maps
• Intrinsic Markov Chains
• GIBBS MEASURES IN ERGODIC THEORY
• Dynamics in One Complex Variable. (AM-160)
• Probability
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
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