Stochastic perturbations of fat solenoidal attractors
type: Item
instance of: scholarly article
title: Stochastic perturbations of fat solenoidal attractors
zbMATH Open document ID: 1209.37043
author: Yan Zheng
publication date: 2010-10-04T00:00:00Z
review text: Consider a skew product transformation, consisting of an angle multiplication by an integer \(l\geq2\) on the unit circle as the base system, and an affine contraction with coefficient \(0<\lambda<1\) of the real line as the fibre system. The base dynamics is assumed to enter the fibre dynamics additively as a \(C^r\), \(r\geq3\), function of the base state. In case that \(\lambda l>1\), i.e.\ if the system is locally area expanding, it is known that there exists an SRB measure which is absolutely continuous with respect to the Lebesgue measure. The present paper gives conditions for the stability of the SRB measure and of its ergodic properties with respect to small stochastic perturbations.
Mathematics Subject Classification ID: 37D99
Mathematics Subject Classification ID: 37C30
Mathematics Subject Classification ID: 37E99
zbMATH DE Number: 5795522
zbMATH Keywords: Sinai-Bowen-Ruelle measure
zbMATH Keywords: SRB measure
zbMATH Keywords: Perron-Frobenius operator
zbMATH Keywords: Lasota-Yorke inequality
reviewed by: Hans Crauel
MaRDI profile type: Publication
full work available at URL: s10114-010-8181-9
OpenAlex ID: W2128727879
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cites work: Q4039910
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cites work: Smooth ergodic theory of random dynamical systems
DOI: 10.1007/S10114-010-8181-9
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published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 5795522