/ 0 10 10 22 v 2 2 8 Fe b 20 01 Poincaré renormalized forms and regular singular points of vector fields in the plane

We discuss the local behaviour of vector fields in the plane R around a regular singular point using a special kind of reduced normal forms recently introduced, i.e. Poincaré renormalized forms [Ann. I.H.P. 70 (1999), 461-514]. We give a complete classification, 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 introduce an alternative scheme of reduction of normal forms, based on Lie algebraic properties, and use it to discuss certain degenerate cases. Both schemes are completely algorithmic, prove to be easy to implement, and only require to solve linear equations.