Abstract

In the study of the cyclicity near an analytic planar center, the Lyapunov quantities and center conditions are closely related. It is well-known that the knowledge of the Lyapunov quantities a precise estimation gives of the cyclicity at the center; furthermore, center conditons can be read from the Lyapunov quantities.

In this talk I present a technique to estimate the cyclicity near the center point, when only a few number of Lyapunov quantities can be calculated. In particular, some constructive algorithms and examples will be shown.

It is joint work with A. Gasull.