A characterization of the generalized Liénard polynomial differential systems having invariant algebraic curves

DOI10.1016/j.chaos.2022.112075zbMath1505.34046OpenAlexW4224884093MaRDI QIDQ2113231

Jaume Llibre, Jaume Giné

Publication date: 12 January 2023

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2022.112075

zbMATH Keywords

invariant algebraic curvefirst integralsLiénard polynomial differential systems

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear ordinary differential equations and systems (34A34) Explicit solutions, first integrals of ordinary differential equations (34A05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Invariant manifolds for ordinary differential equations (34C45)

Related Items (3)

Integrability and solvability of polynomial Liénard differential systems ⋮ Characterization of the Kukles polynomial differential systems having an invariant algebraic curve ⋮ A class of new solvable nonlinear isochronous systems and their classical dynamics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Integrability of dynamical systems: algebra and analysis
• Liénard systems for quadratic systems with invariant algebraic curves
• Invariant algebraic curves for Liénard dynamical systems revisited
• The generalized Liénard polynomial differential systems \(x^\prime = y\), \(y^\prime = - g(x) - f(x) y\) with \(\deg g = \deg f + 1\) are not Liouvillian integrable
• Novel algebraic aspects of Liouvillian integrability for two-dimensional polynomial dynamical systems
• Liouvillian integrability of some quadratic Liénard polynomial differential systems
• Invariant algebraic curves and hyperelliptic limit cycles of Liénard systems
• Puiseux integrability of differential equations
• On the number of hyperelliptic limit cycles of Liénard systems
• Qualitative theory of planar differential systems
• Invariant algebraic curves for the cubic Liénard system with linear damping
• On the hyperelliptic limit cycles of Liénard systems
• Liouvillian first integrals for a class of generalized Liénard polynomial differential systems
• On the local analytic integrability at the singular point of a class of Liénard analytic differential systems
• Liouvillian First Integrals of Differential Equations
• Algebraic invariant curves for the Liénard equation
• Liouvillian first integrals for Liénard polynomial differential systems
• On the Poincaré problem and Liouvillian integrability of quadratic Liénard differential equations
• On the nonexistence of Liouvillian first integrals for generalized Liénard polynomial differential systems
• Liouvillian First Integrals for Generalized Liénard Polynomial Differential Systems

This page was built for publication: A characterization of the generalized Liénard polynomial differential systems having invariant algebraic curves