On the number of limit cycles bifurcating from a non-global degenerated center

DOI10.1016/j.jmaa.2006.06.047zbMath1116.34029OpenAlexW2092128580MaRDI QIDQ868780

Chengzhi Li, Armengol Gasull, Changjian Liu

Publication date: 26 February 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/44148

zbMATH Keywords

limit cycleplanar vector fieldAbelian integraldegenerated center

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)

On the Limit Cycles Bifurcating from Piecewise Quasi-Homogeneous Differential Center ⋮ Zeros of Abelian integrals for a quartic Hamiltonian with figure-of-eight loop through a nilpotent saddle ⋮ The cyclicity of period annuli for a class of cubic Hamiltonian systems with nilpotent singular points ⋮ Estimating the Number of Zeros for Abelian Integrals of Quadratic Reversible Centers with Orbits Formed by Higher-Order Curves ⋮ Bifurcation of Limit Cycles from a Quasi-Homogeneous Degenerate Center ⋮ On the abelian integrals of quadratic reversible centers with orbits formed by genus one curves of higher degree

Cites Work

• Number of zeros of complete elliptic integrals
• The Chebyshev property of elliptic integrals
• Elliptic integrals and their nonoscillation
• A relation between small amplitude and big limit cycles.
• Some lower bounds for \(H(n)\) in Hilbert's 16th problem
• Mathematical problems for the next century
• Singular points and limit cycles of planar polynomial vector fields
• Stability of motion
• Abelian integrals for quadratic centres having almost all their orbits formed by quartics*
• Tangential Hilbert problem for perturbations of hyperelliptic Hamiltonian systems
• On the nonexistence, existence and uniqueness of limit cycles
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• Polynomial systems: a lower bound for the Hilbert numbers
• Averaging analysis of a perturbated quadratic center
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