Giuseppe Gaeta
Poincare' renormalized forms and regular singular points of vector
fields in the plane
(118K, LaTeX)
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.