ON THIRD-ORDER NILPOTENT CRITICAL POINTS: INTEGRAL FACTOR METHOD

DOI10.1142/S0218127411029161zbMath1248.34048OpenAlexW2007346356MaRDI QIDQ3165768

Yi-rong Liu, Ji-Bin Li

Publication date: 19 October 2012

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

Full work available at URL: https://doi.org/10.1142/s0218127411029161

zbMATH Keywords

quasi-Lyapunov constantcenter-focus problemnilpotent critical pointintegral factorbifurcation of limit cycle

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Explicit solutions, first integrals of ordinary differential equations (34A05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Invariant manifolds for ordinary differential equations (34C45)

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Cites Work

• Generating limit cycles from a nilpotent critical point via normal forms
• 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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