Random perturbations of Axiom A basic sets
type: Item
instance of: scholarly article
title: Random perturbations of Axiom A basic sets
zbMATH Open document ID: 0922.58043
DOI: 10.1023/A:1023280407906
author: Peidong Liu
published in: Journal of Statistical Physics
publication date: 1999-10-14T00:00:00Z
review text: This paper concerns random dynamical systems (RDS) generated by small random, diffeomorphism-type perturbations of an Axiom A basic set of a deterministic diffeomorphism. The author is mainly interested in the dynamical properties of such an RDS near the basic set. First of all, the author discusses the structural stability of a hyperbolic set with respect to such time-dependent perturbations. Using the structural stability results and the Markov partition method, the author gives a symbolic representation of the RDS described above when the hyperbolic set is an Axiom A basic set. This enables to apply the thermodynamic formalism of random subshifts of finite type.
Mathematics Subject Classification ID: 37A99
Mathematics Subject Classification ID: 37D99
Mathematics Subject Classification ID: 37C75
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 82B05
zbMATH DE Number: 1279305
zbMATH Keywords: random dynamical system
zbMATH Keywords: SRB measure
zbMATH Keywords: Axiom A basic set
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: a:1023280407906
OpenAlex ID: W1483596341
description: scientific article; zbMATH DE number 1279305