Fine inducing and equilibrium measures for rational functions of the Riemann sphere

DOI10.1007/s11856-015-1257-6zbMath1343.37029OpenAlexW2297883034MaRDI QIDQ891578

Mariusz Urbański, Anna Zdunik, Michał Szostakiewicz

Publication date: 17 November 2015

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11856-015-1257-6

zbMATH Keywords

potentialJulia setHausdorff dimensioncentral limit theoremtopological entropylaw of iterated logarithmKolmogorov-Sinai entropyequilibrium measuretopological pressure

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (8)

Equilibrium states for expanding Thurston maps ⋮ Every complex Hénon map is exponentially mixing of all orders and satisfies the CLT ⋮ Stochastics and thermodynamics for equilibrium measures of holomorphic endomorphisms on complex projective spaces ⋮ Equilibrium states of weakly hyperbolic one-dimensional maps for Hölder potentials ⋮ Thin annuli property and exponential distribution of return times for weakly Markov systems ⋮ The Law of Iterated Logarithm and Equilibrium Measures Versus Hausdorff Measures for Dynamically Semi-regular Meromorphic Functions ⋮ Long hitting times for expanding systems ⋮ Extremality and dynamically defined measures, part II: Measures from conformal dynamical systems

Cites Work

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• Nice inducing schemes and the thermodynamics of rational maps
• Almost sure invariance principle for nonuniformly hyperbolic systems
• Bernoulli coding map and almost sure invariance principle for endomorphisms of \(\mathbb P^k\)
• Harmonic, Gibbs and Hausdorff measures on repellers for holomorphic maps. I
• Recurrence times and rates of mixing
• A proof of Thurston's topological characterization of rational functions
• Parabolic orbifolds and the dimension of the maximal measure for rational maps
• Large entropy measures for endomorphisms of \(\mathbb{CP}^k\)
• On the uniqueness of the density for the invariant measure in an infinite hyperbolic iterated function system
• Stochastics and thermodynamics for equilibrium measures of holomorphic endomorphisms on complex projective spaces
• Analytic families of semihyperbolic generalized polynomial-like mappings
• On Sullivan's conformal measures for rational maps of the Riemann sphere
• On the Perron-Frobenius-ruelle operator for rational maps on the riemann sphere and for Hölder continuous functions
• On the Hyperbolic Hausdorff Dimension of the Boundary of a Basin of Attraction for a Holomorphic Map and of Quasirepellers
• On the Bernoulli property for rational maps
• Convergence of the transfer operator for rational maps
• Statistical properties of equilibrium states for rational maps
• Measures and dimensions in conformal dynamics
• On the transfer operator for rational functions on the Riemann sphere
• Dimensions and Measures in Infinite Iterated Function Systems
• Equilibrium measures for holomorphic endomorphisms of complex projective spaces
• Statistical properties of topological Collet–Eckmann maps
• Ergodic theory of equilibrium states for rational maps

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