Computing center conditions for non-analytic ninth degree vector fields with constant angular speed

DOI10.1186/1687-1847-2012-231zbMath1377.34038OpenAlexW2160060451WikidataQ59289783 ScholiaQ59289783MaRDI QIDQ1690877

Qingjun Ren, Feng Li, Yikun Huang

Publication date: 12 January 2018

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1847-2012-231

zbMATH Keywords

Lyapunov constantcenter-focus problemuniform isochronous centernon-analytic

Mathematics Subject Classification ID

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) Qualitative investigation and simulation of ordinary differential equation models (34C60)

Uses Software

• Mathematica

Cites Work

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• Linearizability conditions of a time-reversible quartic-like system
• Centers and isochronous centers for two classes of generalized seventh and ninth systems
• Classification of the centers and isochronous centers for a class of quartic-like systems
• Classification of the centers, their cyclicity and isochronicity for a class of polynomial differential systems generalizing the linear systems with cubic homogeneous nonlinearities
• Classification of the centers, their cyclicity and isochronicity for the generalized quadratic polynomial differential systems
• Classification of the centers, of their cyclicity and isochronicity for two classes of generalized quintic polynomial differential systems
• Computing center conditions for vector fields with constant angular speed
• Geometry of the uniformly isochronous centers with polynomial commutator

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