Asymptotic expansion of the period function. (Développement asymptotique de la fonction période.) (French) Zbl 0814.34038

Saavedra, Mariana

C. R. Acad. Sci., Paris, Sér. I 319, No. 6, 563-566 (1994).

Summary: Let \(P\) be a polycycle of a vector field in the plane, not necessarily bounded. Suppose that the singularities which appear after desingularization of the vertices are formally linearizable. Consider the function defined by the time of return near the polycycle. The goal of this note is to prove that this function and its derivative have an asymptotic expansion similar to the series of Dulac but with negative powers.

MSC:

34E05	Asymptotic expansions of solutions to ordinary differential equations
34C05	Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C25	Periodic solutions to ordinary differential equations

Keywords:

polycycle; vector field in the plane; singularities; asymptotic expansion