Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mel'nikov Analysis of Homoclinic Chaos in a Perturbed sine-Gordon
  Equation   We describe and characterize rigorously the chaotic behavior of the
sine-Gordon equation. The existence of invariant manifolds and the persistence
of homoclinic orbits for a perturbed sine--Gordon equation are established. We
apply a geometric method based on Mel'nikov's analysis to derive conditions for
the transversal intersection of invariant manifolds of a hyperbolic point of
the perturbed Poincare map.

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The categories of this paper are: math
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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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: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an