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First homoclinic tangencies in the boundary of Anosov diffeomorphisms

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


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