Non-periodic bifurcations for surface diffeomorphisms

Horita, Vanderlei; Muniz, Nivaldo; Sabini, Paulo

doi:10.1090/tran/6168

Non-periodic bifurcations for surface diffeomorphisms
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by Vanderlei Horita, Nivaldo Muniz and Paulo Rogério Sabini PDF

Trans. Amer. Math. Soc. 367 (2015), 8279-8300 Request permission

Abstract:

We prove that a “positive probability” subset of the boundary of the set of hyperbolic (Axiom A) surface diffeomorphisms with no cycles $\mathcal {H}$ 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 $\mathcal {H}$.

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