Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lyapunov graphs of nonsingular Smale flows on $S^{1}\times S^{2}$   In this paper, following J. Franks' work on Lyapunov graphs of nonsingular
Smale flows on $S^3$, we study Lyapunov graphs of nonsingular Smale flows on
$S^1 \times S^2$. More precisely, we determine necessary and sufficient
conditions on an abstract Lyapunov graph to be associated with a nonsingular
Smale flow on $S^1 \times S^2$. We also study the singular type vertices in
Lyapunov graphs of nonsingular Smale flows on 3-manifolds.

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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: supr-con