The sharp bound on the number of zeros of Abelian integral for a perturbation of hyper-elliptic Hamiltonian system

DOI10.1360/012015-2zbMath1488.34229OpenAlexW2415213215MaRDI QIDQ5018049

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Publication date: 17 December 2021

Published in: SCIENTIA SINICA Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1360/012015-2

zbMATH Keywords

abelian integral weak Hilbert's 16th problem hyper-elliptic Hamiltonian

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) 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) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

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