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We construct diffeomorphisms in dimension d ≥ 2 exhibiting C -robust heteroclinic tangencies. Keywords Folding manifolds · Robust equidimensional tangencies · Robust heterodimensional tangencies 1 Introduction An important problem in the modern theory of Dynamical Systems is to describe diffeomorphisms whose qualitative behavior exhibits robustness under (small) per- turbations and how abundant these sets of dynamics can be. Motivated by this issue, Smale (1967) introduced the hyperbolic diffeomorphisms as examples of structural stable dynamics (open sets of dynamics which are all of them conjugated). However, the transverse intersection between the invariant manifolds of basic sets was soon observed as a necessary condition (Williams 1970; Palis 1978; Mañé 1987). The main goal of this article is to study the persistence of the non-transverse intersection between those manifolds. Namely, we focus in tangencial heteroclinic orbits. A diffeomorphism f of a manifold M has a heteroclinic tangency if there are different transitive hyperbolic sets and , points P ∈ , Q ∈ and Y ∈ W ( P) ∩ W (Q) such that def s u c = dim M − dim[T W ( P) + T W (Q)] > 0 and T Y Y def s u d =
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Nov 28, 2019
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