BIFURCATIONS OF CRITICAL PERIODS: CUBIC VECTOR FIELDS IN KAPTEYN'S NORMAL FORM

DOI10.1080/16073606.1999.9632058zbMath0938.34023OpenAlexW2094377216MaRDI QIDQ3836232

Bourama Toni

Publication date: 21 June 2000

Published in: Quaestiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/16073606.1999.9632058

zbMATH Keywords

centercritical periodcubic vector fieldHamiltonian stratumsymmetric stratum

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Normal forms for dynamical systems (37G05) 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) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (2)

Weak Center and Bifurcation of Critical Periods in a Cubic Z₂-Equivariant Hamiltonian Vector Field ⋮ Small amplitude limit cycles and local bifurcation of critical periods for a quartic Kolmogorov system

Cites Work

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• Bifurcation at infinity in polynomial vector fields
• The monotonicity of the period function for planar Hamiltonian vector fields
• Global bifurcation of steady-state solutions
• Quadratic systems with center and their perturbations
• Linearization of isochronous centers
• Local Bifurcation of Critical Periods in Vector Fields With Homogeneous Nonlinearities of the Third Degree
• Local Bifurcations of Critical Periods in the Reduced Kukles System
• Periodic solutions of perturbed second-order autonomous equations

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