Foliations and Polynomial Diffeomorphisms of $\mathbb{R}^{3}$
| dc.creator | Gutierrez, Carlos | |
| dc.creator | Maquera, Carlos | |
| dc.date | 2006-07-17 | |
| dc.date.accessioned | 2026-07-07T07:18:27Z | |
| dc.date.available | 2026-07-07T07:18:27Z | |
| dc.description | Let $Y=(f,g,h):\mathbb{R}^{3} \to \mathbb{R}^{3}$ be a $C^{2}$ map and let $\spec(Y)$ denote the set of eigenvalues of the derivative $DY_p$, when $p$ varies in $\mathbb{R}^3$. We begin proving that if, for some $ε>0,$ $\spec(Y)\cap (-ε,ε)=\emptyset,$ then the foliation $\mathcal{F}(k),$ with $k\in \{f,g,h\},$ made up by the level surfaces $\{k={\rm constant}\},$ consists just of planes. As a consequence, we prove a bijectivity result related to the three-dimensional case of Jelonek's Jacobian Conjecture for polynomial maps of $\mathbb{R}^n.$ | |
| dc.description | 13 pages and 3 figures | |
| dc.identifier | https://arxiv.org/abs/math/0607393 | |
| dc.identifier | http://arxiv.org/abs/math/0607393 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114304 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37C85; 57R30 | |
| dc.title | Foliations and Polynomial Diffeomorphisms of $\mathbb{R}^{3}$ | |
| dc.type | text |