Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stabilization of heterodimensional cycles   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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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph