Godbillon-Vey sequence and Françoise algorithm

DOI10.1016/j.bulsci.2019.02.001zbMath1457.32055arXiv1901.09268OpenAlexW2911454936MaRDI QIDQ2272822

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

Publication date: 16 September 2019

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

Full work available at URL: https://arxiv.org/abs/1901.09268

zbMATH Keywords

deformationsfoliationsGodbillon-Vey sequenceFrançoise algorithm

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Complex vector fields, holomorphic foliations, (mathbb{C})-actions (32M25)

Cites Work

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• A note on a generalization of Françoise's algorithm for calculating higher order Melnikov functions
• Higher order Poincaré-Pontryagin functions and iterated path integrals
• Principal Poincaré-Pontryagin function of polynomial perturbations of the Hamiltonian triangle
• Principal Poincaré-Pontryagin function associated to polynomial perturbations of a product of \((d+1)\) straight lines
• Suites de Godbillon-Vey et intégrales premières. (Godbillon-Vey sequences and first integrals).
• A generalization of Françoise's algorithm for calculating higher order Melnikov functions
• The first nonzero Melnikov function for a family of good divides
• 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

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