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

F. E. Brochero Martinez·L. Lopez-Hernanz
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Abstract

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 $1/n$.

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F. E. Brochero Martinez, L. Lopez-Hernanz. 2007-01-12. Class of the infinitesimal generator of a diffeomorphism in $(\C^m,0)$. https://arxiv.org/abs/math/0701355

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