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

Access to Document

10.1007/s10955-016-1639-0

Fingerprint Dive into the research topics of 'Generalizations of SRB Measures to Nonautonomous, Random, and Infinite Dimensional Systems'. Together they form a unique fingerprint.

Cite this

@article{1d4a8bdef36d45bc8b71f1a9b582ba9e,

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

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}",

year = "2017",

month = feb,

day = "1",

doi = "10.1007/s10955-016-1639-0",

language = "English (US)",

volume = "166",

pages = "494--515",

journal = "Journal of Statistical Physics",

issn = "0022-4715",

publisher = "Springer New York",

number = "3-4",

}

TY - JOUR

T1 - Generalizations of SRB Measures to Nonautonomous, Random, and Infinite Dimensional Systems

AU - Young, Lai Sang

PY - 2017/2/1

Y1 - 2017/2/1

N2 - 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.

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

KW - SRB measures

UR - http://www.scopus.com/inward/record.url?scp=84992147622&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84992147622&partnerID=8YFLogxK

U2 - 10.1007/s10955-016-1639-0

DO - 10.1007/s10955-016-1639-0

M3 - Article

AN - SCOPUS:84992147622

VL - 166

SP - 494

EP - 515

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 3-4

ER -