Equilibrium states for piecewise monotonic transformations

DOI10.1017/S014338570000955XzbMath0499.28012MaRDI QIDQ3964827

Franz Hofbauer, Gerhard Keller

Publication date: 1982

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

periodic orbitsPerron-Frobenius operatorequilibrium statesabsolutely continuous invariant measureslocal specification propertypiecewise monotonic interval transformations

Mathematics Subject Classification ID

Related Items (26)

Smooth Livšic regularity for piecewise expanding maps ⋮ Large deviation principle for piecewise monotonic maps with density of periodic measures ⋮ Counting preimages ⋮ Unique equilibrium states for flows and homeomorphisms with non-uniform structure ⋮ Rigorous statistical procedures for data from dynamical systems ⋮ On the Perron-Frobenius-ruelle operator for rational maps on the riemann sphere and for Hölder continuous functions ⋮ Symbolic dynamics for one dimensional maps with nonuniform expansion ⋮ A Ruelle-Perron-Frobenius theorem for expanding circle maps with an indifferent fixed point ⋮ Local dimension for piecewise monotonic maps on the interval ⋮ Phase transitions for suspension flows ⋮ Stochastic stability in some chaotic dynamical systems ⋮ ENTROPY OF EQUILIBRIUM MEASURES OF CONTINUOUS PIECEWISE MONOTONIC MAPS ⋮ Asymptotic periodicity and banded chaos ⋮ On the Existence of Conformal Measures ⋮ Equilibrium states for interval maps: potentials with \(\sup\varphi- \inf\varphi<h_{\mathrm{top}}(f)\) ⋮ Equilibrium state for one-dimensional Lorenz-like expanding maps ⋮ Long hitting times for expanding systems ⋮ Thermodynamic formalism for random weighted covering systems ⋮ An optimal transportation approach to the decay of correlations for non-uniformly expanding maps ⋮ Fair measure and fair entropy for non-Markov interval maps ⋮ Positive entropy equilibrium states ⋮ Pesin theory and equilibrium measures on the interval ⋮ On the rate of convergence to equilibrium in one-dimensional systems ⋮ Piecewise invertible dynamical systems ⋮ Transience in dynamical systems ⋮ Generalized bounded variation and applications to piecewise monotonic transformations

Cites Work

• On intrinsic ergodicity of piecewise monotonic transformations with positive entropy
• On intrinsic ergodicity of piecewise monotonic transformations with positive entropy. II
• Absolutely continuous measures for certain maps of an interval
• Ergodic properties of invariant measures for piecewise monotonic transformations
• Ergodic theory on compact spaces
• Spectral operators
• The structure of piecewise monotonic transformations
• Examples for the Nonuniqueness of the Equilibrium State

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