Centers and isochronous centers for two classes of generalized seventh and ninth systems

DOI10.1007/s10884-010-9175-0zbMath1222.34032OpenAlexW1992225889MaRDI QIDQ616201

Jaume Llibre, Claudia Valls

Publication date: 7 January 2011

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/226095

zbMATH Keywords

isochronous centercenterAbel equationLyapunov quantitiesreversible center

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) Periodic orbits of vector fields and flows (37C27)

Related Items (7)

Centers for a class of generalized quintic polynomial differential systems ⋮ An algorithmic approach to small limit cycles of nonlinear differential systems: the averaging method revisited ⋮ 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 ⋮ Centers and isochronous centers for generalized quintic systems ⋮ Centers and uniform isochronous centers of planar polynomial differential systems

Cites Work

• Quadratic systems with center and their perturbations
• Algebraic properties of the Lyapunov and period constants
• Limit Cycles for a Class of Abel Equations
• An Abel ordinary differential equation class generalizing known integrable classes
• On a certain generalization of Bautin's theorem
• Algorithmic Derivation of Centre Conditions
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