Dynamical profile of a class of rank-one attractors

Qiudong Wang, Lai-Sang Young

Research output: Contribution to journalArticle

Abstract

This paper contains results on the geometric and ergodic properties of a class of strange attractors introduced by Wang and Young [Towards a theory of rank one attractors. Ann. of Math. (2) 167 (2008), 349-480]. These attractors can live in phase spaces of any dimension, and have been shown to arise naturally in differential equations that model several commonly occurring phenomena. Dynamically, such systems are chaotic; they have controlled non-uniform hyperbolicity with exactly one unstable direction, hence the name rank-one. In this paper we prove theorems on their Lyapunov exponents, Sinai-Ruelle-Bowen (SRB) measures, basins of attraction, and statistics of time series, including central limit theorems, exponential correlation decay and large deviations. We also present results on their global geometric and combinatorial structures, symbolic coding and periodic points. In short, we build a dynamical profile for this class of dynamical systems, proving that these systems exhibit many of the characteristics normally associated with 'strange attractors'.

Original languageEnglish (US)
Pages (from-to)1221-1264
Number of pages44
JournalErgodic Theory and Dynamical Systems
Volume33
Issue number4
DOIs
StatePublished - Aug 2013

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Strange attractor
Chaotic systems
Attractor
Time series
Dynamical systems
Differential equations
Nonuniform Hyperbolicity
Statistics
Basin of Attraction
Periodic Points
Large Deviations
Central limit theorem
Lyapunov Exponent
Phase Space
Coding
Dynamical system
Unstable
Decay
Differential equation
Theorem

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Dynamical profile of a class of rank-one attractors. / Wang, Qiudong; Young, Lai-Sang.

In: Ergodic Theory and Dynamical Systems, Vol. 33, No. 4, 08.2013, p. 1221-1264.

Research output: Contribution to journalArticle

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