The cyclicity of the elliptic segment loops of the reversible quadratic Hamiltonian systems under quadratic perturbations

DOI10.1016/j.jde.2004.04.003zbMath1071.34032OpenAlexW1979756402MaRDI QIDQ704230

Robert Roussarie, Chengzhi Li

Publication date: 13 January 2005

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

Full work available at URL: https://doi.org/10.1016/j.jde.2004.04.003

zbMATH Keywords

limit cyclesbifurcation diagramcyclicity of elliptic segmentsreversible quadratic Hamiltonian systemreversible quadratic Hamiltonian systemssmall quadratic perturbation

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) 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) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (5)

Perturbations of symmetric elliptic Hamiltonians of degree four ⋮ Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems ⋮ Global dynamics of a cubic Hamiltonian system with a periodic annulus linked to equilibria at infinity ⋮ On the number of limit cycles which appear by perturbation of two-saddle cycles of planar vector fields ⋮ Perturbations of quadratic Hamiltonian two-saddle cycles

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