Density of hyperbolicity and tangencies in sectional dissipative regions
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文摘
In this paper we extend the notion of sectionally dissipative periodic points to arbitrarily compact invariant sets. We show that given a sectionally dissipative and attracting region for a diffeomorphisms f, there is a neighborhood of f and a dense subset of it such that any diffeomorphism g in this dense subset either exhibits a sectional dissipative homoclinic tangency or the part of the limit set of g in this attracting region is a hyperbolic compact set. The proof goes extending some results on dominated splitting obtained for compact surfaces maps.

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