Asymptotic stability at infinity for differentiable vector fields of the plane
| dc.creator | Gutierrez, C. | |
| dc.creator | Pires, B. | |
| dc.creator | Rabanal, R. | |
| dc.date | 2006-01-13 | |
| dc.date | 2006-07-19 | |
| dc.date.accessioned | 2026-07-07T06:58:54Z | |
| dc.date.available | 2026-07-07T06:58:54Z | |
| dc.description | Let X:R2\Dr->R2 be a differentiable (but not necessarily C1) vector field, where r>0 and Dr={z\in R2:|z|\le r}. If for some e>0 and for all p\in R2\Dr, no eigenvalue of D_p X belongs to (-e,0]\cup {z\in\C:\mathcal{R}(z)\ge 0}, then (a)For all p\in R2\Dr, there is a unique positive semi--trajectory of X starting at p; (b)\mathcal{I}(X), the index of X at infinity, is a well defined number of the extended real line [-\infty,\infty); (c) There exists a constant vector v\in R2 such that if \mathcal{I}(X) is less than zero (resp. greater or equal to zero), then the point at infinity \infty of the Riemann sphere R2\cup\set{\infty} is a repellor (resp. an attractor) of the vector field X+v. | |
| dc.description | 16 pages, 7 figures | |
| dc.identifier | https://arxiv.org/abs/math/0601341 | |
| dc.identifier | http://arxiv.org/abs/math/0601341 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107547 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 34D23 (Primary) | |
| dc.title | Asymptotic stability at infinity for differentiable vector fields of the plane | |
| dc.type | text |