  We describe a canonical procedure for associating to any (germ of)
holomorphic self-map f of C^n fixing the origin such that df_O is invertible
and non-diagonalizable an n-dimensional complex manifold M, a holomorphic map p
from M to C^n, a point e in M and a (germ of) holomorphic self-map F of M so
that: p restricted to the complement of p^{-1}(O) is a biholomorphism between
this complement and C^n minus the origin; p semiconjugates f and F; and e is a
fixed point of F such that dF_e is diagonalizable. Furthermore, we use this
construction to describe the local dynamics of such an f nearby the origin when
the only eigenvalue of df_O is 1.
