Almost transitive geodesic flows for small perturbations of the round metric on the sphere
by
Howard Weiss
Penn State U
Coauthors: Keith Burns

For any \ep > 0, we construct an explicit smooth Riemannian metric on the sphere Sⁿ, n >= 3, that is within \ep of the round metric and has a geodesic for which the corresponding orbit of the geodesic flow is \ep-dense in the unit tangent bundle. Moreover, for any \ep > 0, we construct a smooth Riemannian metric on Sⁿ, n >= 3, that is within \ep of the round metric and has a geodesic for which the complement of the closure of the corresponding orbit of the geodesic flow has Liouville measure less than \ep.

Date received: March 17, 1998