NON-PERIODIC BIFURCATIONS FOR SURFACE DIFFEOMORPHISMS
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Amer Mathematical Soc
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We prove that a positive probability subset of the boundary of the set of hyperbolic (Axiom A) surface diffeomorphisms with no cycles H is constituted by Kupka-Smale diffeomorphisms: all periodic points are hyperbolic and their invariant manifolds intersect transversally. Lack of hyperbolicity arises from the presence of a tangency between a stable manifold and an unstable manifold, one of which is not associated to a periodic point. All these diffeomorphisms that we construct lie on the boundary of the same connected component of H.
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Transactions Of The American Mathematical Society. Providence: Amer Mathematical Soc, v. 367, n. 12, p. 8279-8300, 2015.
