On the uniqueness of algebraic limit cycles for quadratic polynomial differential systems with two pairs of equilibrium points at infinity

DOI10.1007/s10711-017-0244-yzbMath1395.37015OpenAlexW2609870520MaRDI QIDQ1681810

Claudia Valls, Jaume Llibre

Publication date: 24 November 2017

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/182533

zbMATH Keywords

algebraic limit cyclequadratic polynomial differential system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Stability of solutions to ordinary differential equations (34D20) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Dynamics induced by flows and semiflows (37C10) Periodic orbits of vector fields and flows (37C27)

Related Items (4)

Algebraic limit cycles for quadratic polynomial differential systems ⋮ Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems ⋮ A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems ⋮ Algebraic Limit Cycles on Quadratic Polynomial Differential Systems

Cites Work

• Invariant algebraic curves and rational first integrals of holomorphic foliations in \(\mathbb C P(2)\)
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• The 16th Hilbert problem on algebraic limit cycles
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• Counterexample to a conjecture on the algebraic limit cycles of polynomial vector fields
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• On the 16th Hilbert problem for algebraic limit cycles
• Necessary conditions for the existence of invariant algebraic curves for planar polynomial systems
• Invariant algebraic curves and conditions for a centre
• Invariant algebraic curves and rational first integrals for planar polynomial vector fields
• Uniqueness of algebraic limit cycles for quadratic systems
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