Nilpotence of orbits under monodromy and the length of Melnikov functions
DOI10.1016/j.physd.2021.133017zbMath1493.37057OpenAlexW3196527935MaRDI QIDQ2077618
L. Ortiz-Bobadilla, Jessie Pontigo-Herrera, Dmitri Novikov, Pavao Mardešić
Publication date: 21 February 2022
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.physd.2021.133017
limit cyclesMelnikov functioniterated integralsdisplacement functionabelian integralsnilpotence class
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) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08) Dynamical aspects of holomorphic foliations and vector fields (37F75)
Cites Work
- Higher order Poincaré-Pontryagin functions and iterated path integrals
- Principal Poincaré-Pontryagin function associated to polynomial perturbations of a product of \((d+1)\) straight lines
- Le groupe de monodromie du déploiement des singularités isolées de courbes planes. I
- Suites de Godbillon-Vey et intégrales premières. (Godbillon-Vey sequences and first integrals).
- Infinite orbit depth and length of Melnikov functions
- Free subgroups in linear groups
- The displacement map associated to polynominal unfoldings of planar Hamiltonian vector fields
- Bounding the length of iterated integrals of the first nonzero Melnikov function
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