Relationships between limit cycles and algebraic invariant curves for quadratic systems

DOI10.1016/j.jde.2006.03.013zbMath1109.34025OpenAlexW2000389666MaRDI QIDQ852689

Grzegorz Świrszcz, Jaume Llibre

Publication date: 15 November 2006

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

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

zbMATH Keywords

invariant algebraic curvecofactorisoclinealgebraic limit cycleQuadratic system

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)

Related Items (14)

Quadratic differential systems with complex conjugate invariant lines meeting at a finite point ⋮ Algebraic integrability of foliations of the plane ⋮ Algebraic Limit Cycles Bifurcating from Algebraic Ovals of Quadratic Centers ⋮ Oscillations on one dimensional time dependent center manifolds: algebraic curves approach ⋮ Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems ⋮ Algebraic integrability of planar polynomial vector fields by extension to Hirzebruch surfaces ⋮ The hyperelliptic limit cycles of the Liénard systems ⋮ Number of limit cycles for planar systems with invariant algebraic curves ⋮ The Poincaré problem, algebraic integrability and dicritical divisors ⋮ On the limit cycles bifurcating from an ellipse of a quadratic center ⋮ Algebraic Limit Cycles in Piecewise Linear Differential Systems ⋮ Classification of quadratic systems admitting the existence of an algebraic limit cycle ⋮ A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems ⋮ A class of polynomial planar vector fields with polynomial first integral

Cites Work

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• AN ALGORITHM FOR FINDING INVARIANT ALGEBRAIC CURVES OF A GIVEN DEGREE FOR POLYNOMIAL PLANAR VECTOR FIELDS
• Uniqueness of algebraic limit cycles for quadratic systems

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