Tue05Apr20164:00 pmLewis Hall 101
Department of Mathematics
University of Mississippi
Homoclinic Intersections for Geodesic Flows on Convex Spheres
Transverse homoclinic intersection was discovered by Poincare in the study of stability properties of periodic orbits of n-body problem. Poincare realized that this is a mechanism which not only destroys the stability of periodic orbits but also leads the existence of chaos in the phase space.
In this talk, we will study the geodesic flows on convex spheres. We show that, generically, every closed geodesic is either hyperbolic or irrationally elliptic. Moreover, every hyperbolic closed geodesic admits some transverse homoclinic intersection. Therefore, (everywhere) chaotic dynamics can happen generically on manifolds with simple/trivial topology.