ANALYTIC CENTER OF NILPOTENT CRITICAL POINTS

DOI10.1142/S0218127412501982zbMath1258.34055MaRDI QIDQ4907026

Tao Liu, Feng Li, Lianggang Wu

Publication date: 1 March 2013

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

analytic centerintegrating factorquasi-Lyapunov constantnilpotent critical point

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05)

Related Items (8)

Bi-center problem and bifurcation of limit cycles from nilpotent singular points in \(Z_{2}\)-equivariant cubic vector fields ⋮ A complete classification on the center-focus problem of a generalized cubic Kukles system with a nilpotent singular point ⋮ Limit cycles in a quartic system with a third-order nilpotent singular point ⋮ Bifurcation of limit cycles and center conditions for two families of Kukles-like systems with nilpotent singularities ⋮ Limit cycles and analytic centers for a family of \(4n - 1\) degree systems with generalized nilpotent singularities ⋮ Editorial: Some classes of function spaces, their properties, and their applications 2014 ⋮ Analytic Integrability of Two Lopsided Systems ⋮ Limit cycle bifurcations and analytic center conditions for a class of generalized nilpotent systems

Cites Work

• The analytic and formal normal form for the nilpotent singularity
• Singularities of vector fields
• Generating limit cycles from a nilpotent critical point via normal forms
• BIFURCATIONS OF LIMIT CYCLES CREATED BY A MULTIPLE NILPOTENT CRITICAL POINT OF PLANAR DYNAMICAL SYSTEMS
• NEW STUDY ON THE CENTER PROBLEM AND BIFURCATIONS OF LIMIT CYCLES FOR THE LYAPUNOV SYSTEM (II)
• NEW STUDY ON THE CENTER PROBLEM AND BIFURCATIONS OF LIMIT CYCLES FOR THE LYAPUNOV SYSTEM (I)
• MONODROMY AND STABILITY FOR NILPOTENT CRITICAL POINTS

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