First homoclinic tangencies in the boundary of Anosov diffeomorphisms

Maria Carvalho

doi:10.3934/dcds.1998.4.765

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1998, Volume 4, Issue 4: 765-782. Doi: 10.3934/dcds.1998.4.765

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First homoclinic tangencies in the boundary of Anosov diffeomorphisms

Maria Carvalho¹

1.
Centro de Matemática, Universidade do Porto

Received: June 30, 1996

Revised: August 31, 1997

Published: September 1998

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Abstract

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:

Homoclinic tangencies,
Anosov diffeomorphisms.

Mathematics Subject Classification: Primary: 58F11, 28D05.

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