A unified study on the cyclicity of period annulus of the reversible quadratic Hamiltonian systems

DOI10.1007/s10884-004-2781-yzbMath1077.34036OpenAlexW1987019566MaRDI QIDQ1768350

Chengzhi Li, Jaume Llibre

Publication date: 15 March 2005

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

Full work available at URL: https://doi.org/10.1007/s10884-004-2781-y

zbMATH Keywords

reversible quadratic Hamiltonian systemscyclicity of period annulus

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) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (11)

Limit cycles for perturbing Hamiltonian system inside piecewise smooth polynomial differential system ⋮ The cyclicity of a class of quadratic reversible centers defining elliptic curves ⋮ Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems ⋮ Limit Cycles Bifurcating from a Family of Reversible Quadratic Centers via Averaging Theory ⋮ Quadratic double centers and their perturbations ⋮ Limit cycle bifurcations in perturbations of a reversible quadratic system with a non-rational first integral ⋮ The cyclicity of the elliptic segment loops of the reversible quadratic Hamiltonian systems under quadratic perturbations ⋮ Abelian integrals and limit cycles ⋮ Hilbert’s 16th problem on a period annulus and Nash space of arcs ⋮ Limit cycles bifurcating from the period annulus of quasi-homogeneous centers ⋮ A unified proof of the weakened Hilbert 16th problem for \(n=2\)

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