Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Aperiodicity at the boundary of chaos   We consider the dynamical properties of $C^{\infty}$-variations of the flow
on an aperiodic Kuperberg plug ${\mathbb K}$. Our main result is that there
exists a smooth 1-parameter family of plugs ${\mathbb K}_{\epsilon}$ for
$\epsilon \in (-a,a)$ and $a<1$, such that: (1) The plug ${\mathbb K}_0 =
{\mathbb K}$ is a generic Kuperberg plug; (2) For $\epsilon <0$, the flow in
the plug ${\mathbb K}_{\epsilon}$ has two periodic orbits that bound an
invariant cylinder, all other orbits of the flow are wandering, and the flow
has topological entropy zero; (3) For $\epsilon > 0$, the flow in the plug
${\mathbb K}_{\epsilon}$ has positive topological entropy, and an abundance of
periodic orbits.

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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: physics