Weak Specification Properties and Large Deviations for Non-additive Potentials

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.Comment: 25 pages; accepted by Ergodic Theory and Dynamical System