Normalisation of Poincaré Singularities via Variation of Constants

Timoteo Carletti, Alessandro Margheri, Massimo Villarini

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    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.
    Original languageEnglish
    Pages (from-to)197-212
    Number of pages16
    JournalPublicacións Matemáticas
    Issue number1
    Publication statusPublished - 2005


    • Siegel center problem.
    • Normalization vector fields


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