01-17 Giuseppe Gaeta
Poincare' renormalized forms and regular singular points of vector fields in the plane (118K, LaTeX) Jan 11, 01
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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.

Files: 01-17.src( 01-17.keywords , Prf2d.TEX )