Consequences of contractible geodesics on surfaces

Denvir, J.; Mackay, R.

doi:10.1090/S0002-9947-98-02340-X

Consequences of contractible geodesics on surfaces
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by J. Denvir and R. S. Mackay PDF

Trans. Amer. Math. Soc. 350 (1998), 4553-4568 Request permission

Abstract:

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.

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