Thermodynamic formalism methods in the theory of iteration of mappings in dimension one, real and complex
type: Item
instance of: scholarly article
title: Thermodynamic formalism methods in the theory of iteration of mappings in dimension one, real and complex
zbMATH Open document ID: 1476.37053
author: Feliks Przytycki
published in: Annales Mathematicae Silesianae
publication date: 2021-06-23T00:00:00Z
review text: This survey is focused on the application of thermodynamic formalism to hyperbolic and non-hyperbolic dynamics. In particular, the Hausdorff dimension and the Lyapunov exponents are two main topics of this contribution.
reviewed by: Tao Chen
Mathematics Subject Classification ID: 37D35
Mathematics Subject Classification ID: 37E05
Mathematics Subject Classification ID: 37F10
Mathematics Subject Classification ID: 37F15
Mathematics Subject Classification ID: 37F35
Mathematics Subject Classification ID: 31A20
zbMATH DE Number: 7362512
zbMATH Keywords: one-dimensional dynamics
zbMATH Keywords: geometric pressure
zbMATH Keywords: thermodynamic formalism
zbMATH Keywords: equilibrium states
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: Lyapunov exponents
MaRDI profile type: Publication
full work available at URL: amsil-2020-0023
OpenAlex ID: W3117993557
cites work: Equilibrium states and the ergodic theory of Anosov diffeomorphisms
cites work: Large derivatives, backward contraction and invariant densities for interval maps
cites work: Q4271974
cites work: On the transfer operator for rational functions on the Riemann sphere
cites work: On the Lyapunov spectrum for rational maps
cites work: Lyapunov spectrum for multimodal maps
cites work: On the Makarov law of the iterated logarithm
cites work: A characterization of hyperbolic potentials of rational maps
cites work: On the Existence of Invariant Measures for Piecewise Monotonic Transformations
cites work: The Lyapunov exponent of holomorphic maps
cites work: Hausdorff dimension of harmonic measure on the boundary of an attractive basin for a holomorphic map
cites work: Lyapunov Characteristic Exponents are Nonnegative
cites work: Q4314832
cites work: Conical limit set and Poincaré exponent for iterations of rational functions
cites work: Geometric pressure in real and complex 1-dimensional dynamics via trees of pre-images and via spanning sets
cites work: THERMODYNAMIC FORMALISM METHODS IN ONE-DIMENSIONAL REAL AND COMPLEX DYNAMICS
cites work: Q5240762
cites work: Nice inducing schemes and the thermodynamics of rational maps
cites work: Geometric pressure for multimodal maps of the interval
cites work: Equivalence and topological invariance of conditions for non-uniform hyperbolicity in the iteration of rational maps
cites work: Equality of pressures for rational functions
cites work: Q4384023
cites work: Convergence and pre-images of limit points for coding trees for iterations of holomorphic maps
cites work: Q3563981
cites work: Harmonic, Gibbs and Hausdorff measures on repellers for holomorphic maps. I
cites work: Harmonic, Gibbs and Hausdorff measures on repellers for holomorphic maps, II
cites work: Q4185090
cites work: GIBBS MEASURES IN ERGODIC THEORY
cites work: Q3931654
cites work: Parabolic orbifolds and the dimension of the maximal measure for rational maps
DOI: 10.2478/AMSIL-2020-0023
description: scientific article; zbMATH DE number 7362512