On the number of zeros of Melnikov functions
DOI10.5802/afst.1314zbMath1243.34042arXiv1007.0672OpenAlexW2964329244MaRDI QIDQ650977
Sergey Benditkis, Dmitri Novikov
Publication date: 8 December 2011
Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1007.0672
Hamiltonian systemsMelnikov functionsAbelian integralsLimit cyclesHilbert 16th problemIterated integrals
Bifurcation theory for ordinary differential equations (34C23) Perturbations of ordinary differential equations (34D10) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)
Related Items (2)
Cites Work
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- Higher order Poincaré-Pontryagin functions and iterated path integrals
- On the finite cyclicity of open period annuli
- On the number of zeros of Abelian integrals. A constructive solution of the infinitesimal Hilbert sixteenth problem
- Petrov modules and zeros of abelian integrals
- Equations différentielles à points singuliers réguliers
- Commuting holonomies and rigidity of holomorphic foliations
- Centennial History of Hilbert's 16th Problem
- Modules of the Abelian integrals and the Picard$ndash$Fuchs systems*
- Successive derivatives of a first return map, application to the study of quadratic vector fields
- THE ORIGIN OF LIMIT CYCLES UNDER PERTURBATION OF THE EQUATIONdw/dz= -Rz/Rw, WHERER(z,w) IS A POLYNOMIAL
- Collected papers of K. -T. Chen. Edited by Philippe Tondeur
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