Cyclicity of a class of polynomial nilpotent center singularities

DOI10.3934/dcds.2016.36.2497zbMath1336.37041OpenAlexW2524757267MaRDI QIDQ256217

Douglas S. Shafer, Isaac A. García

Publication date: 9 March 2016

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2016.36.2497

zbMATH Keywords

limit cyclecyclicitynilpotent center

Mathematics Subject Classification ID

Bifurcations of singular points in dynamical systems (37G10) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (7)

On the multiple zeros of a real analytic function with applications to the averaging theory of differential equations ⋮ Examples of center cyclicity bounds using the reduced Bautin depth ⋮ Cyclicity of some symmetric nilpotent centers ⋮ Center cyclicity of a family of quartic polynomial differential system ⋮ Center cyclicity for some nilpotent singularities including the ℤ2-equivariant class ⋮ Cyclicity of nilpotent centers with minimum Andreev number ⋮ The cyclicity of polynomial centers via the reduced Bautin depth

Cites Work

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• Local bifurcation of limit cycles and integrability of a class of nilpotent systems of differential equations
• Direct methods for primary decomposition
• The center-focus problem for a system with homogeneous nonlinearities in the case of zero eigenvalues of the linear part
• Bifurcation of critical periods of polynomial systems
• The center problem for a family of systems of differential equations having a nilpotent singular point
• Stability of motion
• The Center and Cyclicity Problems
• Holonomie et intégrales premières
• Local analytic integrability for nilpotent centers
• The Cyclicity of a Cubic System

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