Control Theory for Semigroups over Local Fields
| dc.creator | Firer, Marcelo | |
| dc.creator | Miranda, Daniel | |
| dc.date | 2007-03-09 | |
| dc.date | 2007-08-27 | |
| dc.date.accessioned | 2026-07-07T08:25:39Z | |
| dc.date.available | 2026-07-07T08:25:39Z | |
| dc.description | Let $G$ be a 1-connected, almost-simple Lie group over a local field and $\mathcal{S}$ a subsemigroup of $G$ with non-empty interior. The action of the regular hyperbolic elements in the interior of $\mathcal{S}$ on the flag manifold $G/P$ and on the associated Euclidean building allows us to prove that the invariant control set exists and is unique. We also provide a characterization of the set of transitivity of the control sets: its elements are the fixed points of type w for a regular hyperbolic isometry, where w is an element of the Weyl group of $G$. Thus, for each w in W there is a control set $D_{w}$ and $W(\mathcal{S})$ the subgroup of the Weyl group such that the control set $D_{w}$ coincides with the invariant control set $D_{1}$ is a Weyl subgroup of $W$. We conclude by showing that the control sets are parameterized by the lateral classes $W(S)\backslash W$. | |
| dc.description | 31 pages; 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0703250 | |
| dc.identifier | http://arxiv.org/abs/math/0703250 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/136694 | |
| dc.subject | Metric Geometry | |
| dc.subject | Optimization and Control | |
| dc.subject | 12J25, 93C99 | |
| dc.title | Control Theory for Semigroups over Local Fields | |
| dc.type | text |