Algebraic limit cycles for quadratic polynomial differential systems

DOI10.3934/dcdsb.2018070zbMath1426.34040OpenAlexW2781883148MaRDI QIDQ1634890

Claudia Valls, Jaume Llibre

Publication date: 18 December 2018

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2018070

zbMATH Keywords

Hilbert's 16th problemalgebraic limit cyclequadratic polynomial differential 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 (3)

Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems ⋮ Number of limit cycles for planar systems with invariant algebraic curves ⋮ A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems

Cites Work

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• On the limit cycles bifurcating from an ellipse of a quadratic center
• Invariant algebraic curves and rational first integrals of holomorphic foliations in \(\mathbb C P(2)\)
• Classification of quadratic systems admitting the existence of an algebraic limit cycle
• Quadratic systems with a unique finite rest point
• On the uniqueness of algebraic limit cycles for quadratic polynomial differential systems with two pairs of equilibrium points at infinity
• Invariant algebraic curves of large degree for quadratic system
• Algebraic limit cycles of degree 4 for quadratic systems
• Necessary conditions for the existence of invariant algebraic curves for planar polynomial systems
• Qualitative theory of planar differential systems
• Invariant algebraic curves and conditions for a centre
• Special issue in celebration of Jack K. Hale's 70th birthday. Part 3 of 4 parts
• Uniqueness of algebraic limit cycles for quadratic systems

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