Linearizability of the polynomial differential systems with a resonant singular point

DOI10.1016/j.bulsci.2006.07.005zbMath1138.34022OpenAlexW2065243412MaRDI QIDQ2472850

Yi-rong Liu, Qin-long Wang

Publication date: 25 February 2008

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2006.07.005

zbMATH Keywords

normal formspolynomial vector fieldssingular point quantitiesgeneralized period constants

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20)

Related Items

Analytic integrability of certain resonant saddle ⋮ On integrability and linearizability of persistent \(p:- q\) resonant systems ⋮ Integrability of fractional order generalized systems with \(p:-q\) resonance ⋮ Linearizability problem of resonant degenerate singular point for polynomial differential systems ⋮ Linearizability of homogeneous quartic polynomial systems with \(1:-2\) resonance ⋮ Complex integrability and linearizability of cubic \(Z_2\)-equivariant systems with two \(1:q\) resonant singular points ⋮ Isochronicity problem of a higher-order singular point for polynomial differential systems ⋮ Integrability and linearizability for Lotka-Volterra systems with the \(3 : -q\) resonant saddle point ⋮ Integrability and generalized center problem of resonant singular point ⋮ Local integrability and linearizability of three-dimensional Lotka-Volterra systems

Uses Software

• Maple
• Mathematica

Cites Work

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• Theory of values of singular point in complex autonomous differential systems
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• The problem of center for resonant singular points of polynomial vector fields
• An explicit expression of the first Lyapunov and period constants with applications
• Quadratic-like cubic systems
• A new method to determine isochronous center conditions for polynomial differential systems.
• Normalizable, integrable, and linearizable saddle points for complex quadratic systems in \(\mathbb{C}^2\)
• Integrability and linearizability of the Lotka-Volterra systems.
• Linearization of isochronous centers
• Isochronous Centers in Planar Polynomial Systems
• Isochronous centers of a linear center perturbed by fifth degree homogeneous polynomials

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