Normalization of Poincaré Singularities \it via Variation of Constants

2004/08/02 by T. Carletti, Carletti, T., A. Margheri +3
Mathematics · #37C05 #37C15 #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 37C10 #Secondary 34C20 #math.DS #msc:34C20 #msc:37C05 #msc:37C10 #msc:37C15

paper · pdf · doi:10.48550/arxiv.math/0408021

arxiv created 2004/08/02 · arxiv updated 2009/12/01

Abstract

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.

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