Nilpotent centres via inverse integrating factors

DOI10.1017/S0956792516000103zbMath1384.34037MaRDI QIDQ4594612

Antonio Algaba, Cristóbal García, Jaume Giné

Publication date: 24 November 2017

Published in: European Journal of Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

integrability problemnon-linear differential systemsnilpotent centre problem

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) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20)

Related Items (10)

The center problem for \(\mathbb{Z}_2\)-symmetric nilpotent vector fields ⋮ Monodromic nilpotent singular points with odd Andreev number and the center problem ⋮ New criterions on stability and order of analytic nilpotent foci ⋮ Nondegenerate and nilpotent centers for a cubic system of differential equations ⋮ Integrability of planar nilpotent differential systems through the existence of an inverse integrating factor ⋮ Limit cycles in a quartic system with a third-order nilpotent singular point ⋮ Center cyclicity for some nilpotent singularities including the ℤ2-equivariant class ⋮ Cyclicity of nilpotent centers with minimum Andreev number ⋮ A new normal form for monodromic nilpotent singularities of planar vector fields ⋮ Orbitally universal centers

Cites Work

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• A new algorithm for determining the monodromy of a planar differential system
• Analytic nilpotent centers as limits of nondegenerate centers revisited
• A class of non-integrable systems admitting an inverse integrating factor
• Existence of inverse integrating factors and Lie symmetries for degenerate planar centers
• Like-linearizations of vector fields
• Center problem for several differential equations via Cherkas' method
• Reversibility and classification of nilpotent centers
• Existence of an inverse integrating factor, center problem and integrability of a class of nilpotent systems
• A method for characterizing nilpotent centers
• Generating limit cycles from a nilpotent critical point via normal forms
• The center problem for a family of systems of differential equations having a nilpotent singular point
• The nondegenerate center problem and the inverse integrating factor
• The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems
• On orbital-reversibility for a class of planar dynamical systems
• Formal Inverse Integrating Factor and the Nilpotent Center Problem
• NEW STUDY ON THE CENTER PROBLEM AND BIFURCATIONS OF LIMIT CYCLES FOR THE LYAPUNOV SYSTEM (II)
• The integrability problem for a class of planar systems
• Symétrie et forme normale des centres et foyers dégénérés
• A note on analytic integrability of planar vector fields
• 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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