Invariant measures on the space of horofunctions of a word hyperbolic group
| dc.creator | Bowen, Lewis Phylip | |
| dc.date | 2007-12-26 | |
| dc.date | 2008-07-15 | |
| dc.date.accessioned | 2026-07-07T09:49:57Z | |
| dc.date.available | 2026-07-07T09:49:57Z | |
| dc.description | We introduce a natural equivalence relation on the space $\sH_0$ of horofunctions of a word hyperbolic group that take the value 0 at the identity. We show that there are only finitely many ergodic measures that are invariant under this relation. This can be viewed as a discrete analog of the Bowen-Marcus theorem. Furthermore, if $η$ is such a measure and $G$ acts on a space $(X,μ)$ by p.m.p. transformations then $η\times μ$ is virtually ergodic with respect to a natural equivalence relation on $\sH_0\times X$. This is comparable to a special case of the Howe-Moore theorem. These results are applied to prove a new ergodic theorem for spherical averages in the case of a word hyperbolic group acting on a finite space. | |
| dc.description | 37 pages. This new version corrects several typos including one in the statement of theorem 1.5 | |
| dc.identifier | https://arxiv.org/abs/0712.4158 | |
| dc.identifier | http://arxiv.org/abs/0712.4158 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164782 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Group Theory | |
| dc.subject | 37A20, 37A15, 20F67 | |
| dc.title | Invariant measures on the space of horofunctions of a word hyperbolic group | |
| dc.type | text |