Integrability of Liénard systems with a weak saddle

DOI10.1007/s00033-016-0756-6zbMath1379.37048OpenAlexW2563291980MaRDI QIDQ2358961

Armengol Gasull, Jaume Giné

Publication date: 27 June 2017

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/182506

zbMATH Keywords

Liénard equationcenter problemweak saddleanalytic integrability

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) Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Formal solutions and transform techniques for ordinary differential equations in the complex domain (34M25)

Related Items

On the integrability of Liénard systems with a strong saddle ⋮ Formal Weierstrass integrability for a Liénard differential system ⋮ On a conjecture on the integrability of Liénard systems ⋮ Integrable weak saddles for trigonometric Liénard systems ⋮ Integrability and solvability of polynomial Liénard differential systems ⋮ Blow-up method to compute necessary conditions of integrability for planar differential systems ⋮ Generalized analytic integrability of a class of polynomial differential systems in \(\mathbb{C}^2\) ⋮ Global solutions to a two-species chemotaxis system with singular sensitivity and logistic source ⋮ Integrability conditions of a weak saddle in a complex polynomial differential system ⋮ Simultaneous integrability and non-linearizability at arbitrary double weak saddles and sole weak focus of a cubic Liénard system

Cites Work

• Integrability conditions of a resonant saddle in Liénard-like complex systems
• On the analytic integrability of the Liénard analytic differential systems
• A method of constructing cycles without contact around a weak focus
• An algebraic approach to the classification of centers in polynomial Liénard systems
• Center problem for several differential equations via Cherkas' method
• Center conditions for polynomial Liénard systems
• On non-integrability of general systems of differential equations
• Small-amplitude limit cycles in polynomial Liénard systems
• Integrability and generalized center problem of resonant singular point
• Stability of motion
• The Center and Cyclicity Problems
• Order of cyclicity of the singular point of lineard's polynomial vector fields
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item