Equivalence of physical and SRB measures in random dynamical systems

Alex Blumenthal, Lai Sang Young

Research output: Contribution to journalArticle

Abstract

We give a geometric proof, offering a new and quite different perspective on an earlier result of Ledrappier and Young on random transformations (Ledrappier and Young 1988 Probab. Theory Relat. Fields 80 217-40). We show that under mild conditions, sample measures of random diffeomorphisms are SRB measures. As sample measures are the limits of forward images of stationary measures, they can be thought of as the analog of physical measures for deterministic systems. Our results thus show the equivalence of physical and SRB measures in the random setting, a hoped-for scenario that is not always true for deterministic maps.

Original languageEnglish (US)
Pages (from-to)1494-1524
Number of pages31
JournalNonlinearity
Volume32
Issue number4
DOIs
StatePublished - Mar 21 2019

Keywords

  • SRB measures
  • physical measures
  • random dynamics

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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