On the Dynamics of G-Solenoids. Applications to Delone Sets
| dc.creator | Benedetti, Riccardo | |
| dc.creator | Gambaudo, Jean-Marc | |
| dc.date | 2002-08-30 | |
| dc.date.accessioned | 2026-07-07T04:50:28Z | |
| dc.date.available | 2026-07-07T04:50:28Z | |
| dc.description | A G-solenoid is a laminated space whose leaves are copies of a single Lie group G, and whose transversals are totally disconnected sets. It inherits a G-action and can be considered as dynamical system. Free Z^d-actions on the Cantor set as well as a large class of tiling spaces possess such a structure of G-solenoid. We show that a G-solenoid can be seen as a projective limit of branched manifolds modeled on G. This allows us to give a topological description of the transverse invariant measures associated with a G-solenoid in terms of a positive cone in the projective limit of the dim(G)-homology groups of these branched manifolds. In particular we exhibit a simple criterion implying unique ergodicity. A particular attention is paid to the case when the Lie group $G$ is the group of affine orientation preserving isometries of the Euclidean space or its subgroup of translations. | |
| dc.description | 26 pages | |
| dc.identifier | https://arxiv.org/abs/math/0208243 | |
| dc.identifier | http://arxiv.org/abs/math/0208243 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64808 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37C40, 22F30, 52C22 | |
| dc.title | On the Dynamics of G-Solenoids. Applications to Delone Sets | |
| dc.type | text |