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• W2951551156 abstract "We consider small polynomial deformations of integrable systems of the form $dF=0$, $Finmathbb{C}[x,y]$ 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." @default.
• W2951551156 created "2019-06-27" @default.
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• W2951551156 date "2017-03-10" @default.
• W2951551156 modified "2023-10-10" @default.
• W2951551156 title "Bounding the length of iterated integrals of the first nonzero Melnikov function" @default.
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