The smallest upper bound on the number of zeros of abelian integrals

DOI10.1016/j.jde.2020.03.016zbMath1464.34057OpenAlexW3011716461MaRDI QIDQ2180598

Changjian Liu, Dongmei Xiao

Publication date: 14 May 2020

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

Full work available at URL: https://doi.org/10.1016/j.jde.2020.03.016

zbMATH Keywords

potential systemsabelian integralconfigurations of limit cyclesnumber of isolated zerossmallest upper bound

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 (6)

The cyclicity of a class of quadratic reversible centers defining elliptic curves ⋮ On the number of limit cycles bifurcating from a quartic reversible center ⋮ Cyclicity of period annulus for a class of quadratic reversible systems with a nonrational first integral ⋮ On the number of limit cycles near a homoclinic loop with a nilpotent cusp of order \(m\) ⋮ A proof of a Dumortier-Roussarie's conjecture ⋮ The Poincaré bifurcation of a SD oscillator

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