Class of the infinitesimal generator of a diffeomorphism in $(\C^m,0)$

Martinez, F. E. Brochero; Lopez-Hernanz, L.

Class of the infinitesimal generator of a diffeomorphism in $(\C^m,0)$

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Description

Let $F$ be an analytic diffeomorphism in $(\C^m,0)$ tangent to the identity of order $n$. The infinitesimal generator of $F$ is the formal vector field $X$ such that $\Exp X=F$. In this paper we provide an elementary proof of the fact that $X$ belongs to the Gevrey class of order $1/n$.
6 pages