Period function monotonicity of planar vector fields

DOI10.1016/J.CAM.2008.05.021zbMath1165.34015OpenAlexW2002034717MaRDI QIDQ2519731

Khalil I. T. Al-Dosary

Publication date: 27 January 2009

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2008.05.021

zbMATH Keywords

monotonicityisochronous centercenterplanar vector fieldperiod function

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)

Cites Work

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• Isochronous centers of Lienard type equations and applications
• The monotonicity of the period function for planar Hamiltonian vector fields
• On period functions of Liénard systems
• An explicit expression of the first Lyapunov and period constants with applications
• Characterizing isochronous centres by Lie brackets
• On the period function of \(x^{\prime\prime}+f(x)x^{\prime2}+g(x)=0\)
• Period function for a class of Hamiltonian systems
• Isochronicity for several classes of Hamiltonian systems
• Linearization of isochronous centers
• Isochronous Centers in Planar Polynomial Systems
• Isochronicity of analytic systems via Urabe's criterion
• regularity properties of the period function near a center of a planar vector field

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