Bautin’s theorem
There are at most three limit cycles which can appear in the following quadratic system
$\dot{x}=p(x,y)$ | $=$ | $\sum _{i+j=0}^{2}}{a}_{ij}{x}^{i}{y}^{j$ | ||
$\dot{y}=q(x,y)$ | $=$ | $\sum _{i+j=0}^{2}}{b}_{ij}{x}^{i}{y}^{j$ |
from a singular point^{}, if its type is either a focus or a center.
References
- 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.
Title | Bautin’s theorem |
---|---|
Canonical name | BautinsTheorem |
Date of creation | 2013-03-22 14:28:46 |
Last modified on | 2013-03-22 14:28:46 |
Owner | Daume (40) |
Last modified by | Daume (40) |
Numerical id | 5 |
Author | Daume (40) |
Entry type | Theorem |
Classification | msc 34C07 |