Abstract:

Given $hge 2$ germs of biholomorphisms of ${mathbb C}^n$ fixing the origin, we investigate
the shape a (formal) simultaneous linearization of the given germs can have, and we prove that
if the germs commute and their linear parts are almost simultaneously Jordanizable then they are
simultaneously formally linearizable.  We next introduce a simultaneous Brjuno-type condition and
prove that, in case the linear terms of the germs are diagonalizable, if the germs commute and our
Brjuno-type condition holds, then they are holomorphically simultaneously linerizable.
This answers to a multi-dimensional version of a problem raised by Moser.