Sulla stabilità di un punto fisso per funzioni di n variabili complesse. Problema del Centro di Schröder-Siegel

Translated title of the contribution: On the stability of a fixed point for functions of n complex variables. The Schröder-Siegel center problem

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    Abstract

    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 contributionOn the stability of a fixed point for functions of n complex variables. The Schröder-Siegel center problem
    Original languageItalian
    Pages (from-to)123-131
    Number of pages9
    JournalBolletino UMI
    Volume8
    Issue number8
    Publication statusPublished - 2005

    Keywords

    • holomorphic dynamics
    • small divisors
    • linearizability

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