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arXiv · 1512.06967

Kupka-Smale diffeomorphisms at the boundary of uniform hyperbolicity: a model

Renaud Leplaideur·Isabel Rios
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Abstract

We construct an explicit example of family of non-uniformly hyperbolic diffeomorphisms, at the boundary of the set of uniformly hyperbolic systems, with one orbit of cubic heteroclinic tangency. One of the leaves involved in this heteroclinic tangency is periodic, and there is a certain degree of freedom for the choice of the second one. For a non-countable set of choices, this leaf is not periodic and the diffeomorphism is Kupka-Smale: every periodic point is hyperbolic and the intersections of stable and unstable leaves of periodic points are transverse. As a consequence of our construction, the map is Hölder conjugated to a subshift of finite type, thus every Hölder potential admits a unique associated equilibrium state.

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Renaud Leplaideur, Isabel Rios. 2015-12-22. Kupka-Smale diffeomorphisms at the boundary of uniform hyperbolicity: a model. https://arxiv.org/abs/1512.06967

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