Planar maps whose second iterate has a unique fixed point
| dc.creator | Alarcón, Begoña | |
| dc.creator | Gutierrez, Carlos | |
| dc.creator | Martínez-Alfaro, José | |
| dc.date | 2007-06-18 | |
| dc.date.accessioned | 2026-07-07T08:10:47Z | |
| dc.date.available | 2026-07-07T08:10:47Z | |
| dc.description | Let a>0, F: R^2 -> R^2 be a differentiable (not necessarily C^1) map and Spec(F) be the set of (complex) eigenvalues of the derivative F'(p) when p varies in R^2. (a) If Spec(F) is disjoint of the interval [1,1+a[, then Fix(F) has at most one element, where Fix(F) denotes the set of fixed points of F. (b) If Spec(F) is disjoint of the real line R, then Fix(F^2) has at most one element. (c) If F is a C^1 map and, for all p belonging to R^2, the derivative F'(p) is neither a homothety nor has simple real eigenvalues, then Fix(F^2) has at most one element, provided that Spec(F) is disjoint of either (c1) the union of the number 0 with the intervals ]-\infty, -1] and [1,\infty[, or (c2) the interval [-1-a, 1+a]. Conditions under which Fix(F^n), with n>1, is at most unitary are considered. | |
| dc.description | 13 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/0706.2580 | |
| dc.identifier | http://arxiv.org/abs/0706.2580 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131921 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 37G10; 37G15; 34K18 | |
| dc.title | Planar maps whose second iterate has a unique fixed point | |
| dc.type | text |