Classification of the centers, their cyclicity and isochronicity for the generalized quadratic polynomial differential systems

DOI10.1016/j.jmaa.2009.04.036zbMath1190.34033OpenAlexW2033743311MaRDI QIDQ1029111

Jaume Llibre, Claudia Valls

Publication date: 9 July 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.04.036

zbMATH Keywords

centersisochronous centerspolynomial vector fieldscyclicity

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)

Related Items (15)

Centers for a class of generalized quintic polynomial differential systems ⋮ Centers and isochronous centers of a class of quasi-analytic switching systems ⋮ Bifurcations of limit circles and center conditions for a class of non-analytic cubic \(Z_2\) polynomial differential systems ⋮ The three-dimensional center problem for the zero-Hopf singularity ⋮ Computing center conditions for non-analytic ninth degree vector fields with constant angular speed ⋮ Integrability and pseudo-linearizable conditions in a quasi-analytic system ⋮ Computing center conditions for non-analytic vector fields with constant angular speed ⋮ Bifurcation of limit cycles and integrability conditions for 6-parameter families of polynomial vector fields of arbitrary degree ⋮ Centers and isochronous centers for generalized quintic systems ⋮ Center cyclicity of a family of quartic polynomial differential system ⋮ Isochronicity and linearizability of a planar cubic system ⋮ Linearizability conditions of a time-reversible quartic-like system ⋮ Complex isochronous centers and linearization transformations for cubic \(Z_2\)-equivariant planar systems ⋮ Bifurcation of limit cycles, classification of centers and isochronicity for a class of non-analytic quintic systems ⋮ LINEAR CENTERS WITH PERTURBATIONS OF DEGREE 2d + 5

Cites Work

• Quadratic systems with center and their perturbations
• Algebraic properties of the Lyapunov and period constants
• Algebraic Particular Integrals, Integrability and the Problem of the Center
• Limit Cycles for a Class of Abel Equations
• Bifurcation of Critical Periods for Plane Vector Fields
• Bifurcation of limit cycles and integrability of planar dynamical systems in complex form
• Quadratic Isochronous centers commute
• Algorithmic Derivation of Centre Conditions
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Classification of the centers, their cyclicity and isochronicity for the generalized quadratic polynomial differential systems