Invariant of topological pressure under some semi-conjugates
type: Item
instance of: scholarly article
title: Invariant of topological pressure under some semi-conjugates
zbMATH Open document ID: 0888.54025
author: Hong Li
author: Winxiang Sun
author: LianFa He
published in: Applied Mathematics. Series B (English Edition)
publication date: 1998-02-19T00:00:00Z
review text: Let \(X,\overline X\) be compact metric spaces, \(f:X\to X\), \(\overline f:\overline X\to\overline X\) continuous maps and \(p:\overline X\to X\) a continuous surjection such that \(p\circ\overline f=f\circ p\). Let \(\varphi:X\to\mathbb{R}\) be a continuous map. In the paper it is shown that the topological pressure \(P(f,\varphi)\) equals the topological pressure \(P(\overline f,\varphi\circ p)\) if one of the following assumptions is satisfied: either \(\overline X\) is a covering space of \(X\) and \(p\) is the covering projection or \((\overline X,\overline f)\) is the inverse limit of \((X,f)\) and \(p\) is the corresponding projection. The result is then applied to obtain a formula for topological entropy of positively expansive maps satisfying specification.
Mathematics Subject Classification ID: 54C70
Mathematics Subject Classification ID: 28D20
Mathematics Subject Classification ID: 37A99
zbMATH DE Number: 1078269
zbMATH Keywords: topological pressure
zbMATH Keywords: topological entropy
zbMATH Keywords: semiconjugacies
reviewed by: Marian Mrozek
MaRDI profile type: Publication
full work available at URL: s11766-997-0036-5
OpenAlex ID: W1973539776
cites work: Some systems with unique equilibrium states
cites work: Entropy for Group Endomorphisms and Homogeneous Spaces
cites work: Statistical Mechanics on a Compact Set with Z p Action Satisfying Expansiveness and Specification
cites work: Q3931654
DOI: 10.1007/S11766-997-0036-5
description: scientific article; zbMATH DE number 1078269