Large deviations for return times in non-rectangle sets for axiom a diffeomorphisms

Renaud Leplaideur; Benoît Saussol

doi:10.3934/dcds.2008.22.327

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2008, Volume 22, Issue 1&2: 327-344. Doi: 10.3934/dcds.2008.22.327

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Large deviations for return times in non-rectangle sets for axiom a diffeomorphisms

Renaud Leplaideur^1, and
Benoît Saussol^1,

1.
Laboratoire de Mathématiques, CNRS UMR 6205, Université de Bretagne Occidentale, 6 av. Victor Le Gorgeu, CS 93837, 29238 BREST Cedex 3

Received: July 2007

Revised: December 2007

Published: March 2008

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Abstract

For Axiom A diffeomorphisms and equilibrium states, we prove a Large deviations result for the sequence of successive return times into a fixed Borel set, under some assumption on the boundary. Our result relies on and extends the work by Chazottes and Leplaideur who considered cylinder sets of a Markov partition.

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Mathematics Subject Classification: Primary: 37B20, 37C45, 37D20, 37D35, 60F10.

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