Multifractal analysis of local entropies for expansive homeomorphisms with specification
type: Item
instance of: scholarly article
title: Multifractal analysis of local entropies for expansive homeomorphisms with specification
zbMATH Open document ID: 0955.37002
author: Evgeny Verbitskiy
author: Floris Takens
published in: Communications in Mathematical Physics
publication date: 1999-12-16T00:00:00Z
full work available at URL: 1999CommMathPhysTakens.pdf
review text: Let \(f\) be an expansive homeomorphism of a compact metric space \(X\), and assume that \(f\) has the specification property. A real-valued function \(\phi\) on \(X\) with appropriate properties will uniquely determine an equilibrium state (Gibbs measure) \(\mu_\phi\), and one can discuss the local entropy function on \(X\) that is determined by \(\mu_\phi\). The central objects studied in the paper are the topological entropies of the restrictions of \(f\) to the level sets of the local entropy function. The main result is a variational relation between this multifractal spectrum and other thermodynamical properties. The results are similar in form to results contained in [\textit{L. Barreira, Ya. Pesin} and \textit{J. Schmeling}, Chaos 7, No. 1, 27-38 (1997; Zbl 0933.37002)], which extend earlier results by Ya. Pesin and H. Weiss. The focus of this earlier work was on local dimensions rather than local entropy.
Mathematics Subject Classification ID: 37A30
Mathematics Subject Classification ID: 28D20
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 37D35
zbMATH DE Number: 1379950
zbMATH Keywords: Gibbs measure
zbMATH Keywords: topological entropies
zbMATH Keywords: local entropy function
zbMATH Keywords: multifractional spectrum
reviewed by: Mike Hurley
MaRDI profile type: Publication
OpenAlex ID: W2074428344
DOI: 10.1007/S002200050627
description: scientific article; zbMATH DE number 1379950