Global properties of tight Reeb flows with applications to Finsler geodesic flows on S 2

摘要: We show that if a Finsler metric on S2 with reversibility r has flag curvatures K satisfying (r/(r+1))2 < ≤ 1, then closed geodesics specific contact-topological properties cannot exist, in particular there are no precisely one transverse self-intersection point. This is special case of more general phenomenon, and other many self-intersections also excluded. provide examples Randers type, obtained by suitably modifying the metrics constructed Katok [21], proving this pinching condition sharp. Our methods borrowed from theory pseudo-holomorphic curves symplectizations. Finally, we study global dynamical aspects 3-dimensional energy levels C2-close to S3