Bifurcation of isolated closed orbits from degenerated singularity in \(\mathbb{R}^{3}\). (English) Zbl 1316.34043
The authors study three-dimensional quasi-homogeneous vector fields having a degenerate singular point at the origin. The main purpose is to estimate the number of isolated periodic trajectories bifurcating from the origin under small analytic one-parameter unfoldings. Lower and upper estimates are provided. Three particular systems are considered as an application.
Reviewer: Iliya Iliev (Sofia)
MSC:
| 34C23 | Bifurcation theory for ordinary differential equations |
| 34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
| 37G15 | Bifurcations of limit cycles and periodic orbits in dynamical systems |
| 34C08 | Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) |
| 34C07 | Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations |
