Large deviations in non-uniformly hyperbolic dynamical systems

Luc Rey-Bellet, Lai-Sang Young

Research output: Contribution to journalArticle

Abstract

We prove large deviation principles for ergodic averages of dynamical systems admitting Markov tower extensions with exponential return times. Our main technical result from which a number of limit theorems are derived is the analyticity of logarithmic moment generating functions. Among the classes of dynamical systems to which our results apply are piecewise hyperbolic diffeomorphisms, dispersing billiards including Lorentz gases, and strange attractors of rank one including Hnon-type attractors.

Original languageEnglish (US)
Pages (from-to)587-612
Number of pages26
JournalErgodic Theory and Dynamical Systems
Volume28
Issue number2
DOIs
StatePublished - Apr 2008

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Large Deviations
Dynamical systems
Dynamical system
Ergodic Averages
Lorentz Gas
Return Time
Strange attractor
Moment generating function
Large Deviation Principle
Billiards
Analyticity
Diffeomorphisms
Limit Theorems
Towers
Attractor
Logarithmic
Gases
Class

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Large deviations in non-uniformly hyperbolic dynamical systems. / Rey-Bellet, Luc; Young, Lai-Sang.

In: Ergodic Theory and Dynamical Systems, Vol. 28, No. 2, 04.2008, p. 587-612.

Research output: Contribution to journalArticle

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