PP-graphics with a nilpotent elliptic singularity in quadratic systems and Hilbert's 16th problem.

DOI10.1016/S0022-0396(03)00119-0zbMath1046.34055OpenAlexW2014760113MaRDI QIDQ1419821

Christiane Rousseau, Huai-Ping Zhu

Publication date: 26 January 2004

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

Full work available at URL: https://doi.org/10.1016/s0022-0396(03)00119-0

zbMATH Keywords

quadratic systemHilbert's 16th problemnilpotent elliptic singularityPP-graphic

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) Dynamics induced by flows and semiflows (37C10) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (10)

Normal forms near a symmetric planar saddle connection ⋮ Bifurcation of limit cycles for a quartic near-Hamiltonian system by perturbing a nilpotent center ⋮ LIMIT CYCLE BIFURCATIONS IN NEAR-HAMILTONIAN SYSTEMS BY PERTURBING A NILPOTENT CENTER ⋮ The loop quantities and bifurcations of homoclinic loops ⋮ Finite cyclicity of elementary graphics surrounding a focus or center in quadratic systems. ⋮ Cyclicity of several planar graphics and ensembles through three singular points without generic conditions ⋮ The full study of planar quadratic differential systems possessing a line of singularities at infinity ⋮ Bifurcation analysis of a generalized Gause model with prey harvesting and a generalized Holling response function of type III ⋮ Analysis on limit cycles of \(Z_{q}\)-equivariant polynomial vector fields with degree 3 or 4 ⋮ Local Limit Cycles of Degenerate Foci in Cubic Systems

Cites Work

• Bifurcations of planar vector fields. Nilpotent singularities and Abelian integrals
• Genericity conditions for finite cyclicity of elementary graphics
• Hilbert's 16th problem for quadratic vector fields
• Finite cyclicity of elementary graphics surrounding a focus or center in quadratic systems.
• Finite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type
• Normal forms near a saddle-node and applications to finite cyclicity of graphics
• On the Structure of Local Homeomorphisms of Euclidean n-Space, II
• Bifurcations of cuspidal loops
• Finitely-smooth normal forms of local families of diffeomorphisms and vector fields
• Elementary graphics of cyclicity 1 and 2
• Hilbert's 16th problem for quadratic systems and cyclicity of elementary graphics
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