Georgia Institute of Technology College of Sciences

In this talk I will present a proof of a generalization of a theorem by Siegel, about the existence of an analytic conjugation between an analytic map, $f(z)=\Lambda z +\hat{f}(z)$, and a linear map, $\Lambda z$, in $\mathbb{C}^n$. This proof illustrates a standar technique used to deal with small divisors problems. I will be following the work of E. Zehnder.