Linearization of germs: regular dependence on the multiplier

Carlo Carminati, Stefano Marmi

We prove that the linearization of a germ of holomorphic map of the type $F_{\lambda }(z)=\lambda (z+O(z^2))$ has a $C^1$--holomorphic dependence on the multiplier $\lambda$. $C^1$--holomorphic functio…