Consequences of Contractible Geodesics on Surfaces

  title={Consequences of Contractible Geodesics on Surfaces},
  author={R. S. MacKay},
The geodesic flow of any Riemannian metric on a geodesically convex surface of negative Euler characteristic is shown to be semi-equivalent to that of any hyperbolic metric on a homeomorphic surface for which the boundary (if any) is geodesic. This has interesting corollaries. For example, it implies chaotic dynamics for geodesic flows on a torus with a simple contractible closed geodesic, and for geodesic flows on a sphere with three simple closed geodesics bounding disjoint discs.