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

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

2004-08-02

arxiv.org/abs/math/0408021v1

Mathematics

Dynamical Systems

Scientific paper

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.

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