Geodesic flows with hyperbolic behaviour of the trajectories and objects connected with them

Abstract

CONTENTS Introduction Part I. Geodesic flows § 1. Preliminary information from differential geometry, topology, and ergodic theory § 2. Local theory § 3. Hyperbolic properties of geodesic flows § 4. The axiom of visibility and the axiom of asymptoticity § 5. Limiting spheres § 6. Topological properties of geodesic flows § 7. Ergodic properties of geodesic flows § 8. Geodesic flows on manifolds of Anosov type Part II. Frame flows and horocycle flows § 9. Definition of a frame flow § 10. Topological and ergodic properties of a frame flow § 11. Definition of the horocycle flow § 12. Topological and ergodic properties of the horocycle flows References