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We prove the holomorphic linearizability of germs of biholomorphisms of (C n, 0), fixing the origin, point at which the linear part has nontrivial Jordanblocks under the following assumptions : We first assume the eigenvalues are ofmodulus less or equal than 1, and that they are non-resonant. We also assumethat they satisfied not only a classical Diophantine condition but also newDiophantine-like conditions related to quasi-resonance phenomena.

On linearization of biholomorphism with non-semi-simple linear part at a fixed point