1 research outputs found
Global properties of tight Reeb flows with applications to Finsler geodesic flows on
We show that if a Finsler metric on with reversibility has flag
curvatures satisfying , then closed geodesics
with specific contact-topological properties cannot exist, in particular there
are no closed geodesics with precisely one transverse self-intersection point.
This is a special case of a more general phenomenon, and other closed geodesics
with many self-intersections are also excluded. We provide examples of Randers
type, obtained by suitably modifying the metrics constructed by Katok
\cite{katok}, proving that this pinching condition is sharp. Our methods are
borrowed from the theory of pseudo-holomorphic curves in symplectizations.
Finally, we study global dynamical aspects of 3-dimensional energy levels
-close to .Comment: 27 page