Normalisation of Poincaré Singularities via Variation of Constants

Timoteo Carletti, Alessandro Margheri, Massimo Villarini

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    Abstract

    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
    Volume49
    Issue number1
    Publication statusPublished - 2005

    Keywords

    • Siegel center problem.
    • Normalization vector fields

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