Weak-foci of high order and cyclicity. (English) Zbl 1396.34018
The authors consider planar polynomial systems in complex form with a weak focus at the origin and study the number of (small) limit cycles bifurcating from the origin under polynomial perturbations.
For this purpose they determine the order of the weak forms which is related to the first non-vanishing Lyapunov number and estimate the cyclicity of the origin (maximum number of bifurcating limit cycles) in dependence of the degree of polynomial perturbations.
For this purpose they determine the order of the weak forms which is related to the first non-vanishing Lyapunov number and estimate the cyclicity of the origin (maximum number of bifurcating limit cycles) in dependence of the degree of polynomial perturbations.
Reviewer: Klaus R. Schneider (Berlin)
MSC:
| 34C07 | Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
Software:
PARI/GPReferences:
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