On the nonexistence of Liouvillian first integrals for generalized Liénard polynomial differential systems

DOI10.1080/14029251.2013.868260zbMath1420.37057OpenAlexW2048924161WikidataQ114098825 ScholiaQ114098825MaRDI QIDQ5230908

Guillaume Chèze, Thomas Cluzeau

Publication date: 29 August 2019

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/14029251.2013.868260

zbMATH Keywords

first integralspolynomial vector fieldsinvariant algebraic curvesLiénard polynomial differential systems

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Structural stability and analogous concepts of solutions to ordinary differential equations (34D30) Relaxation oscillations for ordinary differential equations (34C26)

Related Items (6)

Invariant algebraic curves for Liénard dynamical systems revisited ⋮ The method of Puiseux series and invariant algebraic curves ⋮ Integrability and solvability of polynomial Liénard differential systems ⋮ Invariant algebraic curves for certain generalized Liénard differential system ⋮ Phase portraits of the quadratic polynomial Liénard differential systems ⋮ A characterization of the generalized Liénard polynomial differential systems having invariant algebraic curves

Cites Work

• Unnamed Item
• The limit cycle of the van der Pol equation is not algebraic
• The integration of polynomial Liénard systems by elementary functions
• A general equation for relaxation oscillations
• Elementary First Integrals of Differential Equations
• Liouvillian First Integrals of Differential Equations
• Algebraic invariant curves for the Liénard equation
• Liouvillian first integrals for Liénard polynomial differential systems
• Liouvillian First Integrals for Generalized Liénard Polynomial Differential Systems

This page was built for publication: On the nonexistence of Liouvillian first integrals for generalized Liénard polynomial differential systems