Lyapunov exponents and generalized entropies

Abstract

A relationship which involves, Lyapunov exponents, the ’’fractal dimension of a measure” and one-parameter families of measure-theoretic entropies is established. The relationship is inspired on a one recently reported by Tsallis and collaborators for a physical motivated problem. Also we study the properties of the q—entropy along a foliation, a concept which is introduced in this work as a kind of extension of the Ledrappier and Young definition.