Infinite orbit depth and length of Melnikov functions

DOI10.1016/j.anihpc.2019.07.003zbMath1435.37086arXiv1907.09627OpenAlexW2964776646MaRDI QIDQ2334994

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

Publication date: 13 November 2019

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.09627

zbMATH Keywords

iterated integralscenter problem16-th Hilbert problem

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) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (3)

ZERO BIFURCATION DIAGRAMS FOR ABELIAN INTEGRALS: A STUDY ON HIGHER-ORDER HYPERELLIPTIC HAMILTONIAN SYSTEMS WITH THREE PERTURBATION PARAMETERS ⋮ Nilpotence of orbits under monodromy and the length of Melnikov functions ⋮ Perturbation theory of the quadratic Lotka–Volterra double center

Cites Work

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• Sur la topologie des polynômes complexes. (Topology of complex polynomials)
• The displacement map associated to polynominal unfoldings of planar Hamiltonian vector fields
• Successive derivatives of a first return map, application to the study of quadratic vector fields
• Bounding the length of iterated integrals of the first nonzero Melnikov function

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