Poincare' and Lie renormalized forms for regular singular points of vector fields in the plane
| dc.creator | Gaeta, Giuseppe | |
| dc.date | 2001-01-23 | |
| dc.date | 2002-07-15 | |
| dc.date.accessioned | 2026-07-07T04:28:16Z | |
| dc.date.available | 2026-07-07T04:28:16Z | |
| dc.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. | |
| dc.description | Shortened, streamlined version (with revised title) posted on 15 july 2002; now 35 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0101022 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0101022 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/56721 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Dynamical Systems | |
| dc.title | Poincare' and Lie renormalized forms for regular singular points of vector fields in the plane | |
| dc.type | text |