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

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January & February 2008, 22(1&2): 327-344. doi: 10.3934/dcds.2008.22.327

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, France, France

Received July 2007 Revised December 2007 Published June 2008

Abstract
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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.

Keywords: thermodynamic formalism., large deviations, return times.

Mathematics Subject Classification: Primary: 37B20, 37C45, 37D20, 37D35, 60F1.

Citation: Renaud Leplaideur, Benoît Saussol. Large deviations for return times in non-rectangle sets for axiom a diffeomorphisms. Discrete & Continuous Dynamical Systems - A, 2008, 22 (1&2) : 327-344. doi: 10.3934/dcds.2008.22.327

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