Complex polynomial vector fields having a finitely curved orbit
| dc.creator | Mafra, A. C. | |
| dc.date | 2006-12-05 | |
| dc.date.accessioned | 2026-07-07T07:34:40Z | |
| dc.date.available | 2026-07-07T07:34:40Z | |
| dc.description | In this paper we address the following questions: (i) Let $C\subset \mathbb C^2$ be an orbit of a polynomial vector field which has finite total Gaussian curvature. Is $C$ contained in an algebraic curve? (ii) What can be said of a polynomial vector field which has a finitely curved transcendent orbit? We give a positive answer to (i) under some non-degeneracy conditions on the singularities of the projective foliation induced by the vector field. For vector fields with a slightly more general class of singularities we prove a classification result that captures rational pull-backs of Poincaré-Dulac normal forms. | |
| dc.identifier | https://arxiv.org/abs/math/0612122 | |
| dc.identifier | http://arxiv.org/abs/math/0612122 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119844 | |
| dc.subject | Complex Variables | |
| dc.subject | Differential Geometry | |
| dc.subject | 32M25, 53C42 | |
| dc.title | Complex polynomial vector fields having a finitely curved orbit | |
| dc.type | text |