Fluxos Anosov R-Cobertos

Abstract

In this study we make an introduction to Anosov systems, with special focus on Anosov ows R-covered. We present some basics of: manifolds, groups and group actions, covering spaces and fundamental group; we study the properties of an Anosov flow (...) on a manifold (...), we also analyse properties of stable and unstable foliations associated with this system. Later we study the Anosov flow (...) on the universal covering space (...) induced by (...) on M; also the action of the fundamental group (...) on (...) and on the orbits spaces and leaves space of (...). We present a proof of Verjovsky theorem: a codimension one Anosov flow on a closed n-manifold M (...) is transitive. Finally, we introduce the conceptof foliations and Anosov flows R-covered and study the Anosov system properties. The main references are the work of Thierry Barbot [2], [3] and Sergio Fenley [9].