Stable intersection of Cantor sets in higher dimension and robust homoclinic tangency of the largest codimension
Abstract
In this paper, we construct (a) a pair of two regular Cantor sets in higher dimension which exhibits C1-stable intersection and (b) a hyperbolic basic set which exhibits C2-robust homoclinic tangency of the largest codimension for any higher dimensional manifold, using blenders. The former implies that an analog of Moreira's theorem on Cantor sets in the real line does not hold in higher dimension. The latter solves a question posed by Barrientos and A.Raibekas.
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