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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

Maria Carvalho 1,

1. 

Centro de Matemática, Universidade do Porto, Portugal

Received  July 1996 Revised  September 1997 Published  July 1998

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