The frequency space of a free group
| dc.creator | Kapovich, Ilya | |
| dc.date | 2003-11-05 | |
| dc.date | 2004-08-27 | |
| dc.date.accessioned | 2026-07-07T05:02:37Z | |
| dc.date.available | 2026-07-07T05:02:37Z | |
| dc.description | We analyze the structure of the \emph{frequency space} $Q(F)$ of a nonabelian free group $F=F(a_1,...,a_k)$ consisting of all shift-invariant Borel probability measures on $\partial F$ and construct a natural action of $Out(F)$ on $Q(F)$. In particular we prove that for any outer automorphism $ϕ$ of $F$ the \emph{conjugacy distortion spectrum} of $ϕ$, consisting of all numbers $||ϕ(w)||/||w||$, where $w$ is a nontrivial conjugacy class, is the intersection of $\mathbb Q$ and a closed subinterval of $\mathbb R$ with rational endpoints. We also provide an algorithm for detecting strict hyperbolicity of an automorphism of $F$. | |
| dc.description | Revised version, to appear in IJAC (special issue dedicated to Grigorchuk's 50's birthday) | |
| dc.identifier | https://arxiv.org/abs/math/0311053 | |
| dc.identifier | http://arxiv.org/abs/math/0311053 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69076 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | 20F36 | |
| dc.title | The frequency space of a free group | |
| dc.type | text |