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arxiv: math/0512223 · v1 · submitted 2005-12-11 · 🧮 math.DS

Periodic orbits and homoclinic loops for surface homeomorphisms

classification 🧮 math.DS
keywords pointfixedhomoclinicsurfaceadmittingarcsboundedcell
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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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