Poincar E Renormalized Forms and Regular Singular Points of Vector Elds in the Plane

We discuss the local behaviour of vector elds 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 28]. We give a complete classiication 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.