Resumen de Normalization of Poincairé singularities "via" variation of constants

Alessandro Margheri, Timoteo Carletti, Massimo Villarini

• We present a geometric proof of the Poincaré-Dulac Normalization Theorem for analytic vector fields with singularities of Poincaré 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.