Sharp large deviations for some hyperbolic systems

TL;DR

This paper establishes precise large deviation principles for specific hyperbolic dynamical systems, focusing on the Poincaré map of Axiom A flows, with intervals shrinking at sub-exponential rates.

Contribution

It provides a sharp large deviation result for hyperbolic systems involving the Poincaré map, under regularity assumptions, extending existing large deviation theory.

Findings

Large deviation principles hold for shrinking intervals in hyperbolic systems.

Results apply to Poincaré maps of Axiom A flows on basic sets.

The deviation estimates are sharp and precise.

Abstract

We prove a sharp large deviation principle concerning intervals shrinking with sub-exponential speed for certain models involving the Poincar\'e map related to a Markov family for an Axiom A flow restricted to a basic set $\Lambda$ satisfying some additional regularity assumptions.