Abstract
We show that the loss of hyperbolicity of an Anosov diffeomorphism of the torusT 2 can be produced by a cubic tangency at a heteroclinic point. Such a first bifurcation is generic for 3-parameters families of diffeomorphisms. Our construction may also be applied to any basic set Λ of a surface diffeomorphism. Moreover, if the pointq of cubic tangency corresponds to a lateral point of Λ then the bifurcation is generic for two parameters. In this case the pointq may be a homoclinic intersection.
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Dedicated to the memory of R. Mañé
Partially supported by CNPq (Brazil) and CNRS (France).
Supported by CNRS (France), Rectorat Université de Bourgogne (France) and CNPq (Brazil).
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Bonatti, C., Díaz, L.J. & Vuillemin, F. Cubic tangencies and hyperbolic diffeomorphisms. Bol. Soc. Bras. Mat 29, 99–144 (1998). https://doi.org/10.1007/BF01245870
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DOI: https://doi.org/10.1007/BF01245870