Stable intersection of Cantor sets in higher dimension and robust homoclinic tangency of the largest codimension

2019/11/19 by Masayuki Asaoka, Asaoka, Masayuki
Mathematics · #Analytic and geometric function theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Primary: 37C29 #Secondary: 28A80

paper · pdf · doi:10.48550/arxiv.1911.08091

openalex publication_date 2019/11/19 · openalex created_date 2021/03/01 · openalex updated_date 2026/07/28

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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