Linear estimate of the number of zeros of Abelian integrals for a kind of quartic Hamiltonians

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DOI10.1006/jdeq.1998.3581zbMath0961.34016OpenAlexW2093030779MaRDI QIDQ1293261

Yulin Zhao, Zhi-Fen Zhang

Publication date: 15 September 2000

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.1998.3581

zbMATH Keywords

perturbation limit cycles Hamiltonian periodic solution 16th Hilbert problem

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) 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) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

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