Partições de Markov para automorfismos lineares hiperbólicos do toro

Abstract

This work addresses the study of topological Markov shifts, of hyperbolic toral automorphisms and their relationship. We will be particularly interested in the construction of a Markov partition for these automorphisms. We deal as well with the problem of metric similarity, with a brief discussion of the historic relevance of the topic and showing that a deterministic dynamical system can be metrically similar to a probabilistic one, the latter with positive entropy. This allows us to conclude that deterministic dynamical systems can have positive entropy.