Uma relação entre expoentes de Lyapunov e entropia

Abstract

In this dissertation, we are going to stabilish a relation between Lyapunov exponents, given by Oseledets Multiplicative Ergodic Theorem, and metric entropy, owing to the definition given by Komolgorov-Sinai. For this, we are going to use as tools the study of ergodic’s theory. By the middle, we want to analise and demonstrate the Oseledets multiplicative theorem, that categoryzes the Lyapunov’s expoents of a compact Rimmenian manyfold and finally, introduce the Ruelle’s inequallity, the final result that stabilished the relation between the positive expoents and the metric entropy of a ergodic sistem.