Normal forms and linearization of holomorphic dilation type semigroups   in several variables
  In this paper we study commuting families of holomorphic mappings in $\mathbb{C}^n$ which form abelian semigroups with respect to their real parameter. Linearization models for holomorphic mappings are been used in the spirit of Schr\"oder's classical functional equation. 
Filippo Bracci, Mark Elin, David Shoikhet