Markov extensions for multi-dimensional dynamical systems
type: Item
instance of: scholarly article
title: Markov extensions for multi-dimensional dynamical systems
zbMATH Open document ID: 0988.37012
DOI: 10.1007/BF02773488
author: Jérôme Buzzi
published in: Israel Journal of Mathematics
publication date: 2000-02-01T00:00:00Z
review text: The author proves that an arbitrary piecewise invertible dynamical system is isomorphic ``in the sense of entropy'' with a countable topological Markov chain as soon as one can find some invertibility partition such that a) the topological entropy of the boundary of the partition is smaller than the total topological entropy; b) the partition separates orbits outside some set which is neglibible ``in the sense of entropy''. The author also presents a finiteness result and a nontrivial application to a class of multidimensional dynamical systems. Finally he shows that fibered perturbations of products of chaotic smooth interval maps have a finite number of invariant and ergodic probability measures with maximal entropy.
Mathematics Subject Classification ID: 37A99
Mathematics Subject Classification ID: 37B40
zbMATH DE Number: 1358193
zbMATH Keywords: piecewise invertible dynamical system
zbMATH Keywords: topological entropy
zbMATH Keywords: probability measures
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Entropy for Group Endomorphisms and Homogeneous Spaces
cites work: Intrinsic ergodicity of smooth interval maps
cites work: Intrinsic ergodicity of affine maps in \([0,1]^ d\)
cites work: Ergodicité intrinsèque de produits fibrés d'applications chaotiques unidimensionnelles
cites work: ABSOLUTELY CONTINUOUS INVARIANT MEASURES FOR GENERIC MULTI-DIMENSIONAL PIECEWISE AFFINE EXPANDING MAPS
cites work: Ergodic theory on compact spaces
cites work: Q5590503
cites work: Q5621530
cites work: On intrinsic ergodicity of piecewise monotonic transformations with positive entropy
cites work: Piecewise invertible dynamical systems
cites work: Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
cites work: Markov Extensions, Zeta Functions, and Fredholm Theory for Piecewise Invertible Dynamical Systems
cites work: Lifting measures to Markov extensions
cites work: On a Factor Automorphism of a Normal Dynamical System
cites work: Q5565255
cites work: Q3999363
cites work: Intrinsically ergodic systems
cites work: Volume growth and entropy
full work available at URL: https://doi.org/10.1007/bf02773488
OpenAlex ID: W2008169875
description: scientific article; zbMATH DE number 1358193