Large deviation for return times

TL;DR

This paper establishes a large deviation principle for return times of dynamical system orbits near a point, extending previous work on stationary processes to differentiable systems.

Contribution

It introduces a differentiable version of large deviation results for return times, broadening the scope from stationary processes to dynamical systems.

Findings

Proves a large deviation result for return times in dynamical systems.

Extends previous results from stationary processes to differentiable systems.

Provides a theoretical framework for analyzing return time deviations.

Abstract

We prove a large deviation result for return times of the orbits of a dynamical system in a $r$-neighbourhood of an initial point $x$. Our result may be seen as a differentiable version of the work by Jain and Bansal who considered the return time of a stationary and ergodic process defined in a space of infinite sequences.