Estimates of large deviations in dynamical systems by a non-additive thermodynamic formalism

Abstract

In this article we obtain bounds for large deviations processes in dynamical systems, in which non-additive sequences are considered. More specifically, for sequences [equation] and dynamical maps [equation] such that [equation] converges uniformly we estimate the growing rate of [equation] where n is a finite Borel measure on X and I is a real interval. We consider also a particular case in which the process description easily follows from Ellis theorem.