01-17 Giuseppe Gaeta

Poincare' renormalized forms and regular singular points of vector fields in the plane (118K, LaTeX) Jan 11, 01

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Abstract. We discuss the local behaviour of vector fields in the plane $\R^2$ around a singular point (i.e. a zero), on the basis of standard (Poincar\'e-Dulac) normal forms theory, and from the point of view of Poincar\'e renormalized forms \cite{IHP}. We give a complete classification for regular singular points and provide explicit formulas for non-degenerate cases. A computational error for a degenerate case of codimension 3 contained in previous work is corrected. We also discuss an alternative scheme of reduction of normal forms, based on Lie algebraic properties, and use it to discuss certain degenerate cases.

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