Abstract
We construct an explicit example of a family of non-uniformly hyperbolic diffeomorphisms, at the boundary of a 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 Cantor set of choices of the second one. For a non-countable subset of these choices, the second 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. The bifurcating system is Hölder-conjugated to a subshift of finite type; thus every Hölder potential admits a unique equilibrium state associated with it.
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