Generalizations of SRB Measures to Nonautonomous, Random, and Infinite Dimensional Systems

Research output: Contribution to journalArticle

Abstract

We review some developments that are direct outgrowths of, or closely related to, the idea of SRB measures as introduced by Sinai, Ruelle and Bowen in the 1970s. These new directions of research include the emergence of strange attractors in periodically forced dynamical systems, random attractors in systems defined by stochastic differential equations, SRB measures for infinite dimensional systems including those defined by large classes of dissipative PDEs, quasi-static distributions for slowly varying time-dependent systems, and surviving distributions in leaky dynamical systems.

Original languageEnglish (US)
Pages (from-to)494-515
Number of pages22
JournalJournal of Statistical Physics
Volume166
Issue number3-4
DOIs
StatePublished - Feb 1 2017

Keywords

  • Entropy
  • Infinite dimensional systems
  • Lyapunov exponents
  • Periodic forcing
  • Random perturbations
  • SRB measures

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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