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.

25 pages; accepted by Ergodic Theory and Dynamical Systems

References in corpus (4)

• Lyapunov spectrum of asymptotically sub-additive potentials
• Equilibrium states of the pressure function for products of matrices
• Almost-additive thermodynamic formalism for countable Markov shifts
• Strengthened large deviations for rational maps and full shifts, with unified proof

Cited by in corpus (2)

• Additive, almost additive and asymptotically additive potential sequences are equivalent
• Large Deviations and Fluctuation Theorem for Selectively Decoupled Measures on Shift Spaces