Bifurcation of critical periods from the rigid quadratic isochronous vector field

DOI10.1016/j.bulsci.2007.06.001zbMath1160.34035OpenAlexW1970743197MaRDI QIDQ924913

Yulin Zhao, Armengol Gasull

Publication date: 29 May 2008

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2007.06.001

zbMATH Keywords

isochronous centerbifurcationsperiod functioncritical periods

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)

Related Items (17)

The period function of potential systems of polynomials with real zeros ⋮ A Higher-Order Period Function and Its Application ⋮ Weak Center and Bifurcation of Critical Periods in a Cubic Z₂-Equivariant Hamiltonian Vector Field ⋮ Bifurcation of critical periods from the reversible rigidly isochronous centers ⋮ Weak centers and local bifurcations of critical periods at infinity for a class of rational systems ⋮ Perturbed rigidly isochronous centers and their critical periods ⋮ Number of Critical Periods for Perturbed Rigidly Isochronous Centers ⋮ New lower bound for the number of critical periods for planar polynomial systems ⋮ Local bifurcation of critical periods for a class of Liénard equations ⋮ Critical periods of perturbations of reversible rigidly isochronous centers ⋮ Linearizability and critical period bifurcations of a generalized Riccati system ⋮ Algebraic and analytical tools for the study of the period function ⋮ Critical periods of perturbations of reversible rigidly isochronous centers ⋮ On the period function in a class of generalized Lotka-Volterra systems ⋮ On the number of critical periods for planar polynomial systems of arbitrary degree ⋮ Weak Bi-Center and Critical Period Bifurcations of a Z2-Equivariant Quintic System ⋮ Critical Period Bifurcation by Perturbing a Reversible Rigidly Isochronous Center with Multiple Parameters

Cites Work

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• The monotonicity of period function for the codimension four quadratic system \(Q_4\).
• On the critical periods of perturbed isochronous centers
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• On the monotonicity of the period function of a quadratic system
• On the reversible quadratic centers with monotonic period function
• Bifurcation of Critical Periods for Plane Vector Fields
• Differential Equations Defined by the Sum of two Quasi-Homogeneous Vector Fields
• Finiteness for critical periods of planar analytic vector fields
• On the period function of planar systems with unknown normalizers

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