Stabilization of heterodimensional cycles

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.

31 pages, 9 figures

References in corpus (2)

• Recurrence and genericity
• An example of $C^1$-generically wild homoclinic classes with index deficiency

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