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We are interested in characterizing the holonomy maps associated to integralcurves of non-degenerate singularities of holomorphic vector fields. Such adescription is well-known in dimension 2 where is a key ingredient in the studyof reduced singularities. The most intricate case in the 2 dimensional settingcorresponds to (Siegel) saddle singularities. This work treats the analogousproblem for saddles in higher dimension.  We show that any germ of holomorphic biholomorphism, in any dimension, can beobtained as the holonomy map associated to an integral curve of a saddlesingularity.  A natural question is whether we can prescribe the linear part of the saddlegerm of vector field provided the holonomy map. The answer to this question isknown to be positive in dimension 2. We see that this is not the case in higherdimension. In spite of this, we provide a positive result under a naturalcondition for the holonomy map.

Nondegenerate germs of holomorphic foliations with prescribed holonomy