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Large deviations in non-uniformly hyperbolic dynamical systems

Published online by Cambridge University Press:  01 April 2008

LUC REY-BELLET  and
LAI-SANG YOUNG
LUC REY-BELLET
Affiliation:
Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003, USA (email: [email protected])
LAI-SANG YOUNG
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA (email: [email protected])
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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 Hénon-type attractors.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 2: William Parry Memorial Volume , April 2008 , pp. 587 - 612
Copyright
Copyright © Cambridge University Press 2008

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