Invariant algebraic curves for the cubic Liénard system with linear damping

DOI10.1016/j.bulsci.2006.03.013zbMath1123.34024OpenAlexW2040760581MaRDI QIDQ2500595

Henryk Żołądek, Jaume Llibre, Isaac A. García, Javier Chavarriga

Publication date: 17 August 2006

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2006.03.013

zbMATH Keywords

limit cycleinvariant curveLienard systemalgebraic limit cycle

Mathematics Subject Classification ID

Related Items (10)

Liouvillian integrability versus Darboux polynomials ⋮ Limit cycles in Kukles systems of arbitrary degree with invariant ellipse ⋮ The hyperelliptic limit cycles of the Liénard systems ⋮ Fixed and moving limit cycles for Liénard equations ⋮ Liouvillian integrability of some quadratic Liénard polynomial differential systems ⋮ Periodic solutions of second-order differential equations with two-dimensional Lie point symmetry algebra ⋮ Invariant algebraic curves and hyperelliptic limit cycles of Liénard systems ⋮ Phase portraits of the quadratic polynomial Liénard differential systems ⋮ On the number of hyperelliptic limit cycles of Liénard systems ⋮ A characterization of the generalized Liénard polynomial differential systems having invariant algebraic curves

Cites Work

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• On the integrability of two-dimensional flows
• The limit cycle of the van der Pol equation is not algebraic
• Necessary conditions for the existence of invariant algebraic curves for planar polynomial systems
• Cubic Lienard equations with linear damping
• On the uniqueness of limit cycles surrounding one or more singularities for Liénard equations
• Algebraic invariant curves for the Liénard equation

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