On Plane Polynomial Vector Fields and the Poincare Problem
| dc.contributor.author | El Kahoui, M'hammed | |
| dc.date.accessioned | 2020-08-05T19:06:30Z | |
| dc.date.available | 2020-08-05T19:06:30Z | |
| dc.date.issued | 2002-05-06 | |
| dc.description.abstract | In this paper we address the Poincare problem, on plane polynomial vector fields, under some conditions on the nature of the singularities of invariant curves. Our main idea consists in transforming a given vector field of degree m into another one of degree at most m+1 having its invariant curves in projective quasi-generic position. This allows us to give bounds on degree for some well known classes of curves such as the nonsingular ones and curves with ordinary nodes. We also give a bound on degree for any invariant curve in terms of the maximum Tjurina number of its singularities and the degree of the vector field. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 23 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | El Kahoui, M. (2002). On plane polynomial vector fields and the Poincare problem. Electronic Journal of Differential Equations, 2002(37), pp. 1-23. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/12311 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2002, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Polynomial vector fields | |
| dc.subject | Invariant algebraic curves | |
| dc.subject | Intersection numbers | |
| dc.subject | Tjurina number | |
| dc.subject | Bezout theorem | |
| dc.title | On Plane Polynomial Vector Fields and the Poincare Problem | |
| dc.type | Article |