On the time function of the Dulac map for families of meromorphic vector fields. (English) Zbl 1034.34037
Given an analytic family of vector fields in \({\mathbb R}^2\) having a (common) saddle point. The paper is devoted to the computation of the first terms of the expansion of the time function associated to the Dulac map between transverse sections near the saddle point. The results are applied to the bifurcation of critical periods of quadratic centers.
Reviewer: Marco Spadini (Firenze)
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 |
| 34C25 | Periodic solutions to ordinary differential equations |
| 37C10 | Dynamics induced by flows and semiflows |
| 37C27 | Periodic orbits of vector fields and flows |
