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

DOI10.1016/j.amc.2009.04.077zbMath1201.34061OpenAlexW1971581320MaRDI QIDQ732490

Cristóbal García, Antonio Algaba, Manuel Reyes

Publication date: 9 October 2009

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2009.04.077

zbMATH Keywords

limit cyclecyclicitycenter-focus problemnilpotent critical point

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) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Dynamics induced by flows and semiflows (37C10)

Related Items (10)

Classification and counting of planar quasi-homogeneous differential systems through their weight vectors ⋮ Bifurcation of a piecewise smooth cubic system via expansion of Melnikov function ⋮ On the formal integrability problem for planar differential systems ⋮ Nilpotent systems admitting an algebraic inverse integrating factor over \(\mathbb{C}((x,y))\) ⋮ Cyclicity of some symmetric nilpotent centers ⋮ LIMIT CYCLE BIFURCATION FOR A NILPOTENT SYSTEM IN <i>Z</i>₃-EQUIVARIANT VECTOR FIELD ⋮ Existence of an inverse integrating factor, center problem and integrability of a class of nilpotent systems ⋮ Fourteen limit cycles in a seven-degree nilpotent system ⋮ A method for characterizing nilpotent centers ⋮ Cyclicity of a class of polynomial nilpotent center singularities

Cites Work

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• Center problem for several differential equations via Cherkas' method
• The analytic and formal normal form for the nilpotent singularity
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• The center problem for a family of systems of differential equations having a nilpotent singular point
• The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems
• Stability of motion
• Investigation of the behaviour of the integral curves of a system of two differential equations in the neighbourhood of a singular point
• Local analytic integrability for nilpotent centers
• Symétrie et forme normale des centres et foyers dégénérés
• MONODROMY AND STABILITY FOR NILPOTENT CRITICAL POINTS

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