Invariant measures and uniform positive entropy property for inverse limits
type: Item
instance of: scholarly article
title: Invariant measures and uniform positive entropy property for inverse limits
zbMATH Open document ID: 0944.28015
published in: Applied Mathematics. Series B (English Edition)
publication date: 2000-09-15T00:00:00Z
review text: For a continuous surjective map \(f\) on a compact metric space \(X\), a well-known inverse limit \(\overline {f}\) on the space \(\overline {X}=X^{\infty}\) is associated. The following facts are proven in this paper: (1) The invariant Borel probability measures of \((f,X)\) and \((\overline {f},\overline {X})\) are identical up to a homeomorphism; (2) \((f,X)\) has uniformly positive entropy iff so has \((\overline {f},\overline {X})\). Applications are discussed.
Mathematics Subject Classification ID: 28D20
Mathematics Subject Classification ID: 37A35
Mathematics Subject Classification ID: 37C40
zbMATH DE Number: 1367957
zbMATH Keywords: continuous map
zbMATH Keywords: entropy map
zbMATH Keywords: uniformly positive entropy
author: LianFa He
author: Cuijun Liu
reviewed by: Minping Qian
MaRDI profile type: Publication
full work available at URL: s11766-999-0035-9
OpenAlex ID: W2020635469
cites work: Ergodic theory for axiom A endomorphisms
cites work: Inverse Limits, Entropy and Weak Isomorphism for Discrete Dynamical Systems
cites work: Invariant of topological pressure under some semi-conjugates
cites work: Q3931654
cites work: Ergodic theory on compact spaces
cites work: Some systems with unique equilibrium states
cites work: Q4036997
cites work: Q4297122
DOI: 10.1007/S11766-999-0035-9
description: scientific article; zbMATH DE number 1367957