  We are interested in characterizing the holonomy maps associated to integral
curves of non-degenerate singularities of holomorphic vector fields. Such a
description is well-known in dimension 2 where is a key ingredient in the study
of reduced singularities. The most intricate case in the 2 dimensional setting
corresponds to (Siegel) saddle singularities. This work treats the analogous
problem for saddles in higher dimension.
  We show that any germ of holomorphic biholomorphism, in any dimension, can be
obtained as the holonomy map associated to an integral curve of a saddle
singularity.
  A natural question is whether we can prescribe the linear part of the saddle
germ of vector field provided the holonomy map. The answer to this question is
known to be positive in dimension 2. We see that this is not the case in higher
dimension. In spite of this, we provide a positive result under a natural
condition for the holonomy map.
