Limit at resonances of linearizations of some complex analytic dynamical systems

We consider the behaviour near resonances of Linearizations of germs of hol omorphic diffeomorphisms of (C, 0) and of the semi-standard map. We prove that for each resonance there exists a suitable blow-up of the Tay lor series of the linearization under which it converges uniformly to an an alytic function as the multiplier, or rotation number, tends non-tangential ly to the resonance. This limit function is explicitly computed and related to questions of formal classification, both for the case of germs and for the case of the semi-standard map.