The cyclicity of polynomial centers via the reduced Bautin depth

DOI10.1090/proc/12896zbMath1353.37101OpenAlexW2333449040MaRDI QIDQ2796716

Isaac A. García

Publication date: 29 March 2016

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

Full work available at URL: http://hdl.handle.net/10459.1/57073

zbMATH Keywords

centerlimit cycleBautin idealpolynomial vector fieldscyclicity

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) Dynamics induced by flows and semiflows (37C10) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (1)

Examples of center cyclicity bounds using the reduced Bautin depth

Cites Work

• Cyclicity of a class of polynomial nilpotent center singularities
• Bifurcation of planar vector fields and Hilbert's sixteenth problem
• The reduced Bautin index of planar vector fields
• A necessary condition in the monodromy problem for analytic differential equations on the plane
• Investigation of the behaviour of the integral curves of a system of two differential equations in the neighbourhood of a singular point
• The Center and Cyclicity Problems
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