Bounding the length of iterated integrals of the first nonzero Melnikov function

zbMath1418.34075arXiv1703.03837MaRDI QIDQ4966554

L. Ortiz-Bobadilla, Jessie Pontigo-Herrera, Pavao Mardešić, Dmitri Novikov

Publication date: 26 June 2019

Full work available at URL: https://arxiv.org/abs/1703.03837

zbMATH Keywords

limit cyclescenter problemabelian integralsPoincaré return mapHilbert 16th problemfree group automorphism

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (4)

Analytic moduli for parabolic Dulac germs ⋮ Nilpotence of orbits under monodromy and the length of Melnikov functions ⋮ The first nonzero Melnikov function for a family of good divides ⋮ Infinite orbit depth and length of Melnikov functions

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