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Periodic orbits and homoclinic loops for surface homeomorphisms

Morris W. Hirsch
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Abstract

Let p be a saddle fixed point for an orientation-preserving surface diffeomorphism f admitting a homoclinic point q. Let V be an open 2-cell bounded by a simple loop formed by two arcs joining p to q lying respectively in the stable and unstable curves at p. It is shown that f|V has fixed point index 1 or 2 depending only on the geometry of V near p.

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Morris W. Hirsch. 2005-12-11. Periodic orbits and homoclinic loops for surface homeomorphisms. https://arxiv.org/abs/math/0512223

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