Local bifurcation of limit cycles and integrability of a class of nilpotent systems

DOI10.1186/1687-1847-2012-20zbMath1278.34029OpenAlexW2110819650WikidataQ59290895 ScholiaQ59290895MaRDI QIDQ387284

Yusen Wu, Hong-Wei Li, Yin Lai Jin

Publication date: 20 December 2013

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1847-2012-20

zbMATH Keywords

bifurcation of limit cyclesquasi-Lyapunov constantcenter-focus problemthree-order nilpotent critical point

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Characteristic and Lyapunov exponents of ordinary differential equations (34D08) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (2)

Multiple positive solutions of a \((p_{1},p_{2})\)-Laplacian system with nonlinear BCs ⋮ Some \(q\)-shift difference results on Hayman conjecture and uniqueness theorems

Uses Software

• Mathematica

Cites Work

• Cyclicity versus center problem
• On the structure of Poincaré-Lyapunov constants for the weak focus of polynomial vector fields
• Computation of focus values with applications
• Integrability of centers perturbed by quasi-homogeneous polynomials
• The analytic and formal normal form for the nilpotent singularity
• The center-focus problem for a system with homogeneous nonlinearities in the case of zero eigenvalues of the linear part
• Singularities of vector fields
• A new algorithm for the computation of the Lyapunov constants for some degenerated critical points.
• Generating limit cycles from a nilpotent critical point via normal forms
• The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems
• Stability of motion
• COMPUTATION OF NORMAL FORMS VIA A PERTURBATION TECHNIQUE
• BIFURCATIONS OF LIMIT CYCLES AND CENTER PROBLEM FOR A CLASS OF CUBIC NILPOTENT SYSTEM
• Local analytic integrability for nilpotent centers
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• Degenerate Hopf Bifurcation Formulas and Hilbert’s 16th Problem
• Symétrie et forme normale des centres et foyers dégénérés
• MONODROMY AND STABILITY FOR NILPOTENT CRITICAL POINTS

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