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

TL;DR

This paper establishes a large deviations principle for return times in non-rectangle sets for Axiom A diffeomorphisms, extending previous work on cylinder sets and Markov partitions.

Contribution

It generalizes large deviations results to non-rectangle sets for Axiom A systems, broadening the scope of return time analysis.

Findings

Proves large deviations for return times in non-rectangle sets.

Extends previous results from cylinder sets to more general sets.

Relies on assumptions about the boundary of the sets.

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.