Résumé
We consider the problem of the stability of a fixed point of a germ of
diffeomorphims of several complex variables, by conjugating the system
with its linear part: the Schröder-Siegel centre problem.
We present the problem and some of the main results for the analytic
category. Then we show how to extend the problem to some non--analytic
cases, in particular we will be interested in Gevrey germs. We will
end with an application proving effective stability for a fixed point.
We will point out that an accurate analysis of the problem allows us
to obtain with direct methods, some optimal results obtained by using
the geometrical renormalization ''à la Yoccoz''.
| Titre traduit de la contribution | On the stability of a fixed point for functions of n complex variables. The Schröder-Siegel center problem |
|---|---|
| langue originale | Italien |
| Pages (de - à) | 123-131 |
| Nombre de pages | 9 |
| journal | Bolletino UMI |
| Volume | 8 |
| Numéro de publication | 8 |
| Etat de la publication | Publié - 2005 |