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arXiv · 1104.0980

Stabilization of heterodimensional cycles

Christian Bonatti·Lorenzo J. Diaz·Shin Kiriki
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Abstract

We consider diffeomorphisms $f$ with heteroclinic cycles associated to saddles $P$ and $Q$ of different indices. We say that a cycle of this type can be stabilized if there are diffeomorphisms close to $f$ with a robust cycle associated to hyperbolic sets containing the continuations of $P$ and $Q$. We focus on the case where the indices of these two saddles differ by one. We prove that, excluding one particular case (so-called twisted cycles that additionally satisfy some geometrical restrictions), all such cycles can be stabilized.

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Christian Bonatti, Lorenzo J. Diaz, Shin Kiriki. 2011-04-06. Stabilization of heterodimensional cycles. https://doi.org/10.1088/0951-7715%2F25%2F4%2F931

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