Normalization of Poincaré Singularities {\it via} Variation of Constants

T. Carletti, A. Margheri, M. Villarini

Published 2004-08-02Version 1

We present a geometric proof of the Poincar\'e-Dulac Normalization Theorem for analytic vector fields with singularities of Poincar\'e type. Our approach allows us to relate the size of the convergence domain of the linearizing transformation to the geometry of the complex foliation associated to the vector field. A similar construction is considered in the case of linearization of maps in a neighborhood of a hyperbolic fixed point.