Principal Poincaré-Pontryagin function associated to polynomial perturbations of a product of \((d+1)\) straight lines

DOI10.1016/j.jde.2008.11.014zbMath1173.34026OpenAlexW2051097026MaRDI QIDQ1006089

Marco Uribe

Publication date: 17 March 2009

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2008.11.014

zbMATH Keywords

polynomial systemsdisplacement functionMelnikov functionsAbelian integralscohomology decompositionsPoincare-Pontryagin functions

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) Structure of families (Picard-Lefschetz, monodromy, etc.) (14D05) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (6)

Tangential center problem for a family of non-generic Hamiltonians ⋮ Number of zeros of complete abelian integrals for a primitive rational polynomial with non-trivial global monodromy ⋮ A note on higher order Melnikov functions ⋮ Godbillon-Vey sequence and Françoise algorithm ⋮ Nilpotence of orbits under monodromy and the length of Melnikov functions ⋮ The first nonzero Melnikov function for a family of good divides

Cites Work

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