Bounding the Length of Iterated Integrals of the First Nonzero Melnikov Function

Autor: L. Ortiz-Bobadilla, Pavao Mardešić, Dmitry Novikov, Jessie Pontigo-Herrera

Publikováno v: Moscow Mathematical Journal
Moscow Mathematical Journal, Independent University of Moscow 2018, 18 (2), pp.367-386. ⟨10.17323/1609-4514-2018-18-2-367-386⟩

International audience; 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

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https://hal.archives-ouvertes.fr/hal-01900091