On the definition of SRB-measures for coupled map lattices
type: Item
instance of: scholarly article
title: On the definition of SRB-measures for coupled map lattices
zbMATH Open document ID: 1001.37084
author: Esa Järvenpää
author: Maarit Järvenpää
published in: Communications in Mathematical Physics
publication date: 2002-05-21T00:00:00Z
review text: The authors discuss the different definitions of SRB-measures that have been used in the literature. They show that unlikely for expanding maps on compact manifolds and other nice finite-dimensional systems, the different definitions of SRB-measures in the infinite-dimensional setting are not equivalent and do not give necessarilly an unique measure. For the infinite-dimensional setting the authors define SRB-measures as those having finite-dimensional projections that are absolutely continuous with respect to the corresponding Lebesgue measure. They construct a couple map lattice that exhibits an infinite number of such measures. They show that the multiplicity of SRB-measures exhibited on this example is not a rare behavior. In fact they argue that coupled maps lattices which are closed to an uncoupled expanding map have typically an infinite number of SRB-measures.
reviewed by: Eleonora Catsigeras
Mathematics Subject Classification ID: 37L60
Mathematics Subject Classification ID: 37L40
Mathematics Subject Classification ID: 37D20
Mathematics Subject Classification ID: 37D35
Mathematics Subject Classification ID: 82B05
zbMATH DE Number: 1742836
zbMATH Keywords: SRB-measures
zbMATH Keywords: coupled map lattices
MaRDI profile type: Publication
Wikidata QID: Q110030394
full work available at URL: s002200100432
OpenAlex ID: W2033760001
DOI: 10.1007/S002200100432
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description: scientific article; zbMATH DE number 1742836