Large deviation for return times in open sets for axiom A diffeomorphisms

TL;DR

This paper establishes a large deviation principle for return times in open sets for Axiom A diffeomorphisms with equilibrium states, extending previous results from Markov partitions to more general open sets.

Contribution

It generalizes existing large deviation results from cylinder sets to arbitrary open sets under certain boundary conditions for Axiom A systems.

Findings

Proves a large deviation principle for return times in open sets.

Extends previous work from cylinder sets to general open sets.

Provides conditions on the boundary for the results to hold.

Abstract

For axiom A diffeomorphisms and equilibrium state, we prove a Large deviation result for the sequence of successive return times into a fixed open set, under some assumption on the boundary. Our result relies on and extends the work by Chazottes and Leplaideur who where considering cylinder sets of a Markov partition.