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Bautin's theorem
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(Theorem)
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There are at most three limit cycles which can appear in the following quadratic system
from a singular point, if its type is either a focus or a center.
In 1939 N.N. Bautin claimed the above result and in 1952 submitted the proof [BNN1]. [GAV]
- GAV
- Gaiko, A., Valery: Global Bifurcation Theory and Hilbert's Sixteenth Problem. Kluwer Academic Publishers, London, 2003.
- BNN1
- Bautin, N.N.: On the number of limit cycles appearing from an equilibrium point of the focus or center type under varying coefficients. Matem. SB., 30:181-196, 1952. (written in Russian)
- BNN2
- Bautin, N.N.: On the number of limit cycles appearing from an equilibrium point of the focus or center type under varying coefficients. Translation of the American Mathematical Society, 100, 1954.
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"Bautin's theorem" is owned by Daume.
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(view preamble)
Cross-references: center, singular point, limit cycles
This is version 2 of Bautin's theorem, born on 2004-07-20, modified 2008-05-08.
Object id is 6011, canonical name is BautinsTheorem.
Accessed 2391 times total.
Classification:
| AMS MSC: | 34C07 (Ordinary differential equations :: Qualitative theory :: Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramif) |
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Pending Errata and Addenda
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