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arXiv · 1103.3255

Fragile cycles

Christian Bonatti·Lorenzo J. Diaz
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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 $\Difr(\SS^2\times \SS^1)$, $r\ge 1$, that consists of diffeomorphisms with fragile heterodimensional cycles. Our construction holds for any manifold of dimension $\ge 4$.

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Christian Bonatti, Lorenzo J. Diaz. 2011-03-16. Fragile cycles. https://arxiv.org/abs/1103.3255

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