The Markus-Yamabe Conjecture for Differentiable vector fields of R^2
| dc.creator | Gutierrez, Carlos | |
| dc.creator | Rabanal, Roland | |
| dc.date | 2003-11-21 | |
| dc.date | 2004-08-13 | |
| dc.date.accessioned | 2026-07-07T05:03:09Z | |
| dc.date.available | 2026-07-07T05:03:09Z | |
| dc.description | (a) Let X=(f,g) be a differentiable map in the plane (not necessarily C^1) and let Spec(X) be the set of (complex) eigenvalues of the derivative DX(p) when p varies in R^2. If, for some ε>0, the set Spec(X) is disjoint of [0,ε) then X is injective. (b) Let X be a differentiable vector field such that X(0)=0 and $Re(z)< 0$ for all z in Spec(X). Then, for all p in R^2, there is a unique positive trajectory starting at p; moreover the ω-limit set of p is equal to {0}. | |
| dc.description | ABSTRACT | |
| dc.identifier | https://arxiv.org/abs/math/0311386 | |
| dc.identifier | http://arxiv.org/abs/math/0311386 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69300 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 26B10, 34D23, 34D45 (Primary); 34D20 (Secondary) | |
| dc.title | The Markus-Yamabe Conjecture for Differentiable vector fields of R^2 | |
| dc.type | text |