Recurrence times and large deviations

TL;DR

This paper introduces a criterion for determining large deviation rate functions in abstract dynamical systems and applies it to establish a level 2 large deviation principle for certain nonuniform hyperbolic interval maps.

Contribution

It provides a new criterion for large deviation rate functions and demonstrates its application to specific classes of dynamical systems.

Findings

Established a criterion for large deviation rate functions.

Proved the level 2 large deviation principle for some smooth interval maps.

Extended large deviation theory to nonuniform hyperbolic systems.

Abstract

We give a criterion to determine the large deviation rate functions for abstract dynamical systems on towers. As an application of this criterion we show the level 2 large deviation principle for some class of smooth interval maps with nonuniform hyperbolicity.