`a`
Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

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

Pages: 327 - 344, Volume 22, Issue 1/2, September/October 2008

doi:10.3934/dcds.2008.22.327       Abstract        Full Text (260.1K)       Related Articles

Renaud Leplaideur - Laboratoire de Mathématiques, CNRS UMR 6205, Université de Bretagne Occidentale, 6 av. Victor Le Gorgeu, CS 93837, 29238 BREST Cedex 3, France (email)
Benoît Saussol - Laboratoire de Mathématiques, CNRS UMR 6205, Université de Bretagne Occidentale, 6 av. Victor Le Gorgeu, CS 93837, 29238 BREST Cedex 3, France (email)

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.

Keywords:  large deviations, return times, thermodynamic formalism.
Mathematics Subject Classification:  Primary: 37B20, 37C45, 37D20, 37D35, 60F10.

Received: July 2007;      Revised: December 2007;      Published: June 2008.