Transitividade topológica do fluxo geodésico em variedades riemannianas sem pontos conjugados

Abstract

This dissertation treat the study of the transitivity of geodesic ows on Riemannian manifolds without conjugate points. Based on studies performed by Eberlein in [7], which extended the results obtained in various research, dedicated to proving the topological transitivity of geodesic ows on compact manifolds with curvature K 6 0, requiring that the manifolds were of uniform visibility. We can consider the visibility of manifold M, SM the unit tangent bundle M and 't the geodesic ow in SM, results were presented and developed to show that every point of SM is not wandering through 't then 't is topologically transitive on SM. Lastly we present situations that do not occur transitivity [2] and visibility [20].