Classification of Invariant Algebraic Curves and Nonexistence of Algebraic Limit Cycles in Quadratic Systems from Family (I) of the Chinese Classification

DOI10.1142/S021812742050056XzbMath1446.34047OpenAlexW3016543712MaRDI QIDQ5107088

Maria V. Demina, Claudia Valls

Publication date: 22 April 2020

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s021812742050056x

zbMATH Keywords

invariant algebraic curvePoincaré problemDarboux polynomialalgebraic limit cycle

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Explicit solutions, first integrals of ordinary differential equations (34A05) Invariant manifolds for ordinary differential equations (34C45)

Related Items (1)

Liouvillian integrability and the Poincaré problem for nonlinear oscillators with quadratic damping and polynomial forces

Cites Work

• Invariant algebraic curves for Liénard dynamical systems revisited
• Resolution of the Poincaré problem and nonexistence of algebraic limit cycles in family (I) of Chinese classification
• Novel algebraic aspects of Liouvillian integrability for two-dimensional polynomial dynamical systems
• Qualitative theory of planar differential systems
• Algebraic invariant curves for the Liénard equation
• Asymptotic behaviour and expansions of solutions of an ordinary differential equation
• On a Result of Darboux
• On the Poincaré problem and Liouvillian integrability of quadratic Liénard differential equations
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