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

DOI10.1016/j.bulsci.2004.03.012zbMath1274.37012OpenAlexW2089616008MaRDI QIDQ707254

Pavao Mardešić, Michèle Pelletier, Ahmed Jebrane

Publication date: 9 February 2005

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

Full work available at URL: https://doi.org/10.1016/j.bulsci.2004.03.012

Mathematics Subject Classification ID

Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Dynamics induced by flows and semiflows (37C10)

Related Items (10)

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 ⋮ A note on 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 ⋮ Periodic orbits from second order perturbation via rational trigonometric integrals

Cites Work

• Unnamed Item
• A generalization of Françoise's algorithm for calculating higher order Melnikov functions
• On cyclicity of triangles and segments in quadratic systems
• The cyclicity of the period annulus of the quadratic Hamiltonian triangle
• Successive derivatives of a first return map, application to the study of quadratic vector fields
• Algebras of Iterated Path Integrals and Fundamental Groups

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