On the algebraic structure and the number of zeros of abelian integral for a class of Hamiltonians with degenerate singularities

DOI10.1007/s00574-018-0085-9zbMath1447.34034OpenAlexW2802263760WikidataQ114228893 ScholiaQ114228893MaRDI QIDQ1757112

Jihua Yang

Publication date: 2 January 2019

Published in: Bulletin of the Brazilian Mathematical Society. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00574-018-0085-9

zbMATH Keywords

Picard-Fuchs equationdegenerate singularityabelian integralChebyshev space

Mathematics Subject Classification ID

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)

Related Items (1)

The Number of Zeros of Abelian Integral for a Quintic Hamiltonian Systems With a Rose-Figure Loop

Cites Work

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• Bifurcation of limit cycles from a Liénard system with a heteroclinic loop connecting two nilpotent saddles
• The cyclicity of period annuli of a class of quintic Hamiltonian systems
• An explicit linear estimate for the number of zeros of Abelian integrals
• An improved estimate for the number of zeros of Abelian integrals for cubic Hamiltonians
• Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians
• On the Number of Limit Cycles Bifurcated from Some Hamiltonian Systems with a Double Homoclinic Loop and a Heteroclinic Loop
• Complex zeros of an elliptic integral

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