Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounding the length of iterated integrals of the first nonzero Melnikov
  function   We consider small polynomial deformations of integrable systems of the form
$dF=0$, $F\in\mathbb{C}[x,y]$ and the first nonzero term $M_\mu$ of the
displacement function $\Delta(t,\epsilon)=\sum_{i=\mu}M_i(t)\epsilon^i$ along a
cycle $\gamma(t)\in F^{-1}(t)$. It is known that $M_\mu$ is an iterated
integral of length at most $\mu$. The bound $\mu$ depends on the deformation of
$dF$.
  In this paper we give a universal bound for the length of the iterated
integral expressing the first nonzero term $M_\mu$ depending only on the
topology of the unperturbed system $dF=0$. The result generalizes the result of
Gavrilov and Iliev providing a sufficient condition for $M_\mu$ to be given by
an abelian integral i.e. by an iterated integral of length $1$. We conjecture
that our bound is optimal.

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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol