On Linearization of Biholomorphism with Non-semi-simple Linear Part at a Fixed Point

Abstract

We prove the holomorphic linearizability of germs of biholomorphisms of $$(\mathbb {C}^n,0)$$ , fixing the origin, point at which the linear part has nontrivial Jordan blocks under the following assumptions: the eigenvalues are of modulus less or equal than 1, are non-resonant and satisfy not only a classical Diophantine condition but also new Diophantine-like conditions related to quasi-resonance phenomena.