Highest weak focus order for trigonometric Liénard equations

DOI10.1007/s10231-019-00936-8zbMath1450.34022OpenAlexW2993370751MaRDI QIDQ778062

Claudia Valls, Armengol Gasull, Jaume Giné

Publication date: 30 June 2020

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-019-00936-8

zbMATH Keywords

weak focuscyclicitytrigonometric Liénard equation

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

Small-amplitude limit cycles of certain planar differential systems, Global dynamics of the Josephson equation in \(TS^1\), On the existence and uniqueness of limit cycles for hybrid oscillators

Cites Work

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• On the number of limit cycles for perturbed pendulum equations
• A simple solution of some composition conjectures for Abel equations
• Bifurcation formulae derived from center manifold theory
• An algebraic approach to the classification of centers in polynomial Liénard systems
• An explicit expression of the first Lyapunov and period constants with applications
• Bifurcation of planar vector fields and Hilbert's sixteenth problem
• Implementation of a new algorithm of computation of the Poincaré-Lyapunov constants.
• Limit cycles in the equation of whirling pendulum with autonomous perturbation.
• Small-amplitude limit cycles in polynomial Liénard systems
• Small-amplitude limit cycles in Liénard systems via multiplicity
• Center problem for trigonometric Liénard systems
• A new approach to the computation of the Lyapunov constants
• On some open problems in planar differential systems and Hilbert's 16th problem
• An explicit bound of the number of vanishing double moments forcing composition
• Limit Cycles in the Josephson Equation
• The Bautin ideal of the Abel equation
• Small-amplitude limit cycle bifurcations for Liénard systems with quadratic or cubic damping or restoring forces
• Integrable systems in the plane with center type linear part
• On a condition for a centre of cubic non-autonomous equations
• Universal centres and composition conditions
• Algorithmic Derivation of Centre Conditions