Integrability conditions of a resonant saddle in Liénard-like complex systems

DOI10.1016/j.chaos.2015.11.026zbMath1355.34056OpenAlexW2193234208MaRDI QIDQ508901

Claudia Valls, Jaume Giné

Publication date: 8 February 2017

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

Full work available at URL: http://hdl.handle.net/10459.1/58373

zbMATH Keywords

first integralsanalytic integrabilityintegrable saddles

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)

Related Items (9)

Integrability of Liénard systems with a weak saddle ⋮ Integrability of resonant saddles in a complex differential system ⋮ Analytic integrability of certain resonant saddle ⋮ On the integrability of Liénard systems with a strong saddle ⋮ Integrability conditions of a resonant saddle in generalized Liénard-like complex polynomial differential systems ⋮ Integrability conditions of a weak saddle in generalized Liénard-like complex polynomial differential systems ⋮ Blow-up method to compute necessary conditions of integrability for planar differential systems ⋮ 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

• On the formal integrability problem for planar differential systems
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• Integrability conditions for Lotka-Volterra planar complex quintic systems
• An algebraic approach to the classification of centers in polynomial Liénard systems
• The problem of center for resonant singular points of polynomial vector fields
• Normalizable, integrable, and linearizable saddle points for complex quadratic systems in \(\mathbb{C}^2\)
• On some open problems in planar differential systems and Hilbert's 16th problem
• The Center and Cyclicity Problems
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• Centers for the Kukles homogeneous systems with odd degree
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