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''.
|Translated title of the contribution||On the stability of a fixed point for functions of n complex variables. The Schröder-Siegel center problem|
|Number of pages||9|
|Publication status||Published - 2005|
- holomorphic dynamics
- small divisors