Center conditions for a class of planar rigid polynomial differential systems

DOI10.3934/dcds.2015.35.1075zbMath1308.34038OpenAlexW1987334526MaRDI QIDQ477396

Roland Rabanal, Jaume Llibre

Publication date: 3 December 2014

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2015.35.1075

zbMATH Keywords

limit cyclesisochronous centersfocal basisLyapunov quantitiesthe center problem

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) 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 (7)

An eigenvalue condition and the equivalence of two-dimensional maps ⋮ Rigid centres on the center manifold of tridimensional differential systems ⋮ Bifurcation of piecewise smooth manifolds from 3D center-type vector fields ⋮ Hopf bifurcation at infinity and dissipative vector fields of the plane ⋮ Center conditions for generalized polynomial Kukles systems ⋮ Uniformly isochronous quartic systems ⋮ Limit Cycles on Piecewise Smooth Vector Fields with Coupled Rigid Centers

Cites Work

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• The center-focus problem and small amplitude limit cycles in rigid systems
• Planar real polynomial differential systems of degree \(n> 3\) having a weak focus of high order
• Symbolic computation and the cyclicity problem for singularities
• An explicit expression of the first Lyapunov and period constants with applications
• Conditions for a centre in a simple class of cubic systems
• Bifurcation of planar vector fields and Hilbert's sixteenth problem
• Center conditions for a simple class of quintic systems
• Limit cycles for rigid cubic systems
• Über das Auftreten von Wirbeln und Strudeln (geschlossener und spiraliger Integralkurven) in der Umgebung rationaler Unbestimmtheitsstellen
• Centers with degenerate infinity and their commutators.
• Computing center conditions for vector fields with constant angular speed
• Algebraic conditions for a centre or a focus in some simple systems of arbitrary degree
• Cyclicity of a family of vector fields
• Stability of motion
• On the center conditions of certain cubic systems
• Degenerate Hopf Bifurcation Formulas and Hilbert’s 16th Problem
• Exact number of limit cycles for a family of rigid systems
• Algorithmic Derivation of Centre Conditions
• ON INTEGRABILITY OF DIFFERENTIAL EQUATIONS DEFINED BY THE SUM OF HOMOGENEOUS VECTOR FIELDS WITH DEGENERATE INFINITY
• Probleme General de la Stabilite du Mouvement. (AM-17)
• Commutators and linearizations of isochronous centers

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