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

Lai Sang Young

doi:10.1007/s10955-016-1639-0

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

Lai Sang Young

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	494-515
Number of pages	22
Journal	Journal of Statistical Physics
Volume	166
Issue number	3-4
DOIs	https://doi.org/10.1007/s10955-016-1639-0
State	Published - 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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10.1007/s10955-016-1639-0

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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.",

keywords = "Entropy, Infinite dimensional systems, Lyapunov exponents, Periodic forcing, Random perturbations, SRB measures",

author = "Young, {Lai Sang}",

note = "Funding Information: This research is partially supported by NSF Grant DMS-1363161.",

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AB - 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.

KW - Entropy

KW - Infinite dimensional systems

KW - Lyapunov exponents

KW - Periodic forcing

KW - Random perturbations

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

Abstract

Keywords

ASJC Scopus subject areas

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