Limit cycles and analytic centers for a family of \(4n - 1\) degree systems with generalized nilpotent singularities

DOI10.1155/2015/859015zbMath1332.34065OpenAlexW2030190673WikidataQ59112905 ScholiaQ59112905MaRDI QIDQ492598

Yusen Wu, Cui Zhang, Chang-Jin Xu

Publication date: 20 August 2015

Published in: Journal of Function Spaces (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2015/859015

zbMATH Keywords

limit cycleanalytic centerautonomous polynomial planar systemnilpotent singular pointquasi-Lyapunov 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) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Uses Software

• Mathematica

Cites Work

• Unnamed Item
• Analytic nilpotent centers with analytic first integral
• Analytic integrability and characterization of centers for generalized nilpotent singular points.
• Singularities of vector fields
• The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems
• ON THIRD-ORDER NILPOTENT CRITICAL POINTS: INTEGRAL FACTOR METHOD
• Investigation of the behaviour of the integral curves of a system of two differential equations in the neighbourhood of a singular point
• Symétrie et forme normale des centres et foyers dégénérés
• ANALYTIC CENTER OF NILPOTENT CRITICAL POINTS
• The center-focus problem and reversibility

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