Principal part of multi-parameter displacement functions

DOI10.1016/J.BULSCI.2012.02.006zbMath1258.34057OpenAlexW2030474708MaRDI QIDQ713127

Marco Uribe, Pavao Mardešić, Mariana Saavedra

Publication date: 26 October 2012

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2012.02.006

zbMATH Keywords

limit cyclesMelnikov functionBautin idealiterated integralsdisplacement functionabelian integralsstandard basis

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Uses Software

• SINGULAR

Cites Work

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• Unfolding of the Hamiltonian triangle vector field
• A note on a generalization of Françoise's algorithm for calculating higher order Melnikov functions
• Higher order Poincaré-Pontryagin functions and iterated path integrals
• Perturbations of symmetric elliptic Hamiltonians of degree four
• Iterated integrals, Gelfand-Leray residue, and first return mapping
• Quadratic systems with center and their perturbations
• Perturbations of quadratic centers
• Bifurcation of planar vector fields and Hilbert's sixteenth problem
• A generalization of Françoise's algorithm for calculating higher order Melnikov functions
• Higher-order Melnikov functions for degenerate cubic Hamiltonians
• The cyclicity of the period annulus of the quadratic Hamiltonian triangle
• The displacement map associated to polynominal unfoldings of planar Hamiltonian vector fields
• Cyclicity of period annuli and principalization of Bautin ideals
• Successive derivatives of a first return map, application to the study of quadratic vector fields
• SINGULAR
• Melnikov functions and Bautin ideal

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