Bifurcation of limit cycles in cubic integrable \(Z_{2}\)-equivariant planar vector fields

DOI10.1007/s12346-010-0025-6zbMath1214.34027OpenAlexW2124023824MaRDI QIDQ611139

Pei Yu, Ji-Bin Li, Mao'an Han

Publication date: 14 December 2010

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12346-010-0025-6

zbMATH Keywords

limit cyclefocal valueHilbert's sixteenth problemcenter bifurcation

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Symmetries, invariants of ordinary differential equations (34C14) Bifurcation theory for ordinary differential equations (34C23) Bifurcations of singular points in dynamical systems (37G10) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (2)

Hopf bifurcation of limit cycles in discontinuous Liénard systems ⋮ Limit cycle bifurcations in a class of quintic \(Z_2\)-equivariant polynomial systems

Cites Work

• Unnamed Item
• A cubic system with thirteen limit cycles
• Bifurcation set and limit cycles forming compound eyes in a perturbed Hamiltonian system
• On Hopf cyclicity of planar systems
• Small limit cycles bifurcating from fine focus points in cubic order \(Z_{2}\)-equivariant vector fields
• COMPUTATION OF NORMAL FORMS VIA A PERTURBATION TECHNIQUE
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• TWELVE LIMIT CYCLES IN A CUBIC CASE OF THE 16th HILBERT PROBLEM
• On hereditarily indecomposable Banach spaces

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