A generalization of Françoise's algorithm for calculating higher order Melnikov functions

DOI10.1016/S0007-4497(02)01138-7zbMath1029.34081OpenAlexW2024476209MaRDI QIDQ1865247

Michèle Pelletier, Ahmed Jebrane, Pavao Mardešić

Publication date: 26 March 2003

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

Full work available at URL: https://doi.org/10.1016/s0007-4497(02)01138-7

zbMATH Keywords

limit cycleAbelian integralMilnor fibrationMelnikov functionsFrançoise's algorithmFuchs system

Mathematics Subject Classification ID

Structure of families (Picard-Lefschetz, monodromy, etc.) (14D05) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Oscillation, growth of solutions to ordinary differential equations in the complex domain (34M10)

Related Items (16)

Higher order Poincaré-Pontryagin functions and iterated path integrals ⋮ BIFURCATION CURVES OF SUBHARMONIC SOLUTIONS AND MELNIKOV THEORY UNDER DEGENERACIES ⋮ Iterated integrals, Gelfand-Leray residue, and first return mapping ⋮ Principal Poincaré-Pontryagin function of polynomial perturbations of the Hamiltonian triangle ⋮ Number of zeros of complete abelian integrals for a primitive rational polynomial with non-trivial global monodromy ⋮ Heteroclinic bifurcation of limit cycles in perturbed cubic Hamiltonian systems by higher-order analysis ⋮ The number of limit cycles bifurcating from the period annulus of quasi-homogeneous Hamiltonian systems at any order ⋮ A note on higher order Melnikov functions ⋮ The inverse integrating factor and the Poincaré map ⋮ A note on a generalization of Françoise's algorithm for calculating higher order Melnikov functions ⋮ Principal part of multi-parameter displacement functions ⋮ Godbillon-Vey sequence and Françoise algorithm ⋮ Hilbert’s 16th problem on a period annulus and Nash space of arcs ⋮ Principal Poincaré-Pontryagin function associated to polynomial perturbations of a product of \((d+1)\) straight lines ⋮ Melnikov functions of arbitrary order for piecewise smooth differential systems in \(\mathbb{R}^n\) and applications ⋮ The first nonzero Melnikov function for a family of good divides

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• Quelques calculs de cohomologie relative
• THE ORIGIN OF LIMIT CYCLES UNDER PERTURBATION OF THE EQUATIONdw/dz= -R_z/R_w, WHERER(z,w) IS A POLYNOMIAL

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