  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 H\"older conjugated to a subshift of finite type, thus every H\"older
potential admits a unique associated equilibrium state.

Dynamical Systems