Quasigeodesic Anosov flows and homotopic properties of flow lines

A nonsingular flow is quasigeodesic when all flow lines are efficient in measuring distances in relative homotopy classes. We analyze quasigeodesic Anosov flows in 3-manifolds which have negatively curved fundamental group. We prove that the lifts of the stable and unstable foliations to the universal cover are foliations with branching, that is, they have non-Hausdorff leaf space. Furthermore any branching is associated to freely homotopic closed orbits of the flow in the manifold and there are finitely many such branching leaves up to covering translations. Using this we prove that the limit sets of the stable and unstable leaves in the universal cover cannot be Jordan curves nor the whole sphere. Identifications of ideal points of leaves are also described using freely homotopic orbits. Finally, for any Anosov flow in such manifolds, we prove the existence of uncountably many (infinitely many of which are closed) Kquasigeodesic orbits for K big enough. The key tool is the analysis of freely homotopic closed orbits, which are completely characterized for general Anosov flows.