Fragile cycles

2011/03/16 by Bonatti, Christian, Diaz, Lorenzo J.
#37C29 #37D20 #37D30 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1103.3255

Abstract

We study diffeomorphisms f with heterodimensional cycles, that is, heteroclinic cycles associated to saddles p and q with different indices. Such a cycle is called fragile if there is no diffeomorphism close to f with a robust cycle associated to hyperbolic sets containing the continuations of p and q. We construct a codimension one submanifold of \Difr(\SS²× \SS¹), r≥ 1, that consists of diffeomorphisms with fragile heterodimensional cycles. Our construction holds for any manifold of dimension ≥ 4.

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