Examples of center cyclicity bounds using the reduced Bautin depth

DOI10.1090/proc/13570zbMath1390.37085OpenAlexW2559494868MaRDI QIDQ5351796

Isaac A. García

Publication date: 30 August 2017

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/13570

zbMATH Keywords

limit cycleBautin idealcyclicitypolynomial vector field

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)

Cites Work

• Cyclicity of a class of polynomial nilpotent center singularities
• Smooth equivalence of germs of vector fields with a single zero eigenvalue or a pair of purely imaginary eigenvalues
• Bifurcation of planar vector fields and Hilbert's sixteenth problem
• The reduced Bautin index of planar vector fields
• The Hopf cyclicity of the centers of a class of quintic polynomial vector fields
• The cyclicity of polynomial centers via the reduced Bautin depth
• The Center and Cyclicity Problems
• Generating Ideals up to Projective Equivalence
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