Periodic orbits and homoclinic loops for surface homeomorphisms

Details Periodic orbits and homoclinic loops for surface homeomorphisms Periodic orbits and homoclinic loops for surface homeomorphisms

2005-12-11

arxiv.org/abs/math/0512223v1

Michigan Mathematics Journal 47 (2000) 395-406

Mathematics

Dynamical Systems

Slight correction of published version. 13 pages

Scientific paper

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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