Weak Specification Properties and Large Deviations for Non-additive Potentials

TL;DR

This paper establishes large deviation bounds for deviation sets in dynamical systems with weak specification properties, including hyperbolic systems, and explores implications for Lyapunov exponents.

Contribution

It introduces large deviation principles for asymptotically additive and sub-additive potentials under weak specification, extending previous results to broader classes of systems.

Findings

Large deviation bounds are derived for non-additive potentials.

A large deviation principle is proved for uniformly hyperbolic systems.

Connections to Lyapunov exponent convergence are demonstrated.

Abstract

We obtain large deviation bounds for the measure of deviation sets associated to asymptotically additive and sub-additive potentials under some weak specification properties. In particular a large deviation principle is obtained in the case of uniformly hyperbolic dynamical systems. Some examples in connection with the convergence of Lyapunov exponents are given.