An explicit linear estimate for the number of zeros of Abelian integrals

DOI10.1088/0951-7715/25/6/1931zbMath1277.34039arXiv1108.1846OpenAlexW2020767744MaRDI QIDQ2895598

Gal Binyamini, Gal Dor

Publication date: 3 July 2012

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.1846

zbMATH Keywords

limit cycleabelian integralinfinitesimal Hilbert's sixteenth problem

Mathematics Subject Classification ID

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 (5)

Limit cycle enumeration in random vector fields ⋮ Zeros of Abelian integrals for a quartic Hamiltonian with figure-of-eight loop through a nilpotent saddle ⋮ On the algebraic structure and the number of zeros of abelian integral for a class of Hamiltonians with degenerate singularities ⋮ The cyclicity of period annuli for a class of cubic Hamiltonian systems with nilpotent singular points ⋮ On the number of zeros of Abelian integral for a class of cubic Hamiltonian systems

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