We present a geometric proof of the Poincare-Dulac Normalization Theorem for analytic vector fields with singularities of Poincare 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.
Normalization of Poincare' singularities via variation of constants / T., Carletti; A., Margheri; Villarini, Massimo. - In: PUBLICACIONS MATEMÀTIQUES. - ISSN 0214-1493. - STAMPA. - 49:1(2005), pp. 197-212. [10.5565/PUBLMAT_49105_09]
Normalization of Poincare' singularities via variation of constants
VILLARINI, Massimo
2005
Abstract
We present a geometric proof of the Poincare-Dulac Normalization Theorem for analytic vector fields with singularities of Poincare 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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