First homoclinic tangencies in the boundary of Anosov diffeomorphisms

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October 1998, 4(4): 765-782. doi: 10.3934/dcds.1998.4.765

First homoclinic tangencies in the boundary of Anosov diffeomorphisms

1.	Centro de Matemática, Universidade do Porto, Portugal

Received July 1996 Revised September 1997 Published July 1998

Abstract
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In dimension two, there are no paths from an Anosov diffeomorphism reaching the boundary of the stability components while attaining a first quadratic tangency associated to a periodic point. Therefore we analyse the possibility to construct an arc ending with a first cubic homoclinic tangency. For several reasons that will be explained in the sequel, we will restrict to area preserving diffeomorphisms.

Keywords: Anosov diffeomorphisms., Homoclinic tangencies.

Mathematics Subject Classification: Primary: 58F11, 28D0.

Citation: Maria Carvalho. First homoclinic tangencies in the boundary of Anosov diffeomorphisms. Discrete & Continuous Dynamical Systems - A, 1998, 4 (4) : 765-782. doi: 10.3934/dcds.1998.4.765

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