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arXiv · 1601.07079

Homoclinic intersections for geodesic flows on convex spheres

Zhihong Xia·Pengfei Zhang
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Abstract

In this paper we study some generic properties of the geodesic flows on a convex sphere. We prove that, $C^r$ generically ($2\le r\le\infty$), every hyperbolic closed geodesic admits some transversal homoclinic orbits.

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Zhihong Xia, Pengfei Zhang. 2016-01-26. Homoclinic intersections for geodesic flows on convex spheres. https://doi.org/10.1090/conm%2F698%2F13980

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