Poincare' and Lie renormalized forms for regular singular points of vector fields in the plane
Abstract
Description
We discuss the local behaviour of vector fields in the plane $\R^2$ around a regular singular point, using recently introduced reduced normal forms, i.e. Poincaré and Lie renormalized forms [{\it Lett. Math. Phys.} {\bf 42} (1997), 103-114; {\it Ann. Inst. H. Poincaré (Phys. Theo.)} {\bf 70} (1999), 461-514; {\it Lett. Math. Phys.} {\bf 57} (2001), 41-60]. We give a complete classification, and provide explicit formulas, using Poincaré renormalized forms for non-degenerate cases, and Lie ones for certain degenerate cases. Both schemes are completely algorithmic, prove to be easy to implement, and only require to solve linear equations.
Shortened, streamlined version (with revised title) posted on 15 july 2002; now 35 pages
Shortened, streamlined version (with revised title) posted on 15 july 2002; now 35 pages