The Subadditive Ergodic Theorem and generic stretching factors for free group automorphisms
| dc.creator | Kaimanovich, Vadim | |
| dc.creator | Kapovich, Ilya | |
| dc.creator | Schupp, Paul | |
| dc.date | 2005-04-06 | |
| dc.date.accessioned | 2026-07-07T05:18:50Z | |
| dc.date.available | 2026-07-07T05:18:50Z | |
| dc.description | Given a free group $F_k$ of rank $k\ge 2$ with a fixed set of free generators we associate to any homomorphism $ϕ$ from $F_k$ to a group $G$ with a left-invariant semi-norm a generic stretching factor, $λ(ϕ)$, which is a non-commutative generalization of the translation number. We concentrate on the situation when $ϕ:F_k\to Aut(X)$ corresponds to a free action of $F_k$ on a simplicial tree $X$, in particular, when $ϕ$ corresponds to the action of $F_k$ on its Cayley graph via an automorphism of $F_k$. In this case we are able to obtain some detailed ``arithmetic'' information about the possible values of $λ=λ(ϕ)$. We show that $λ\ge 1$ and is a rational number with $2kλ\in \mathbb Z[ \frac{1}{2k-1} ]$ for every $ϕ\in Aut(F_k)$. We also prove that the set of all $λ(ϕ)$, where $ϕ$ varies over $Aut(F_k)$, has a gap between 1 and $1+\frac{2k-3}{2k^2-k}$, and the value 1 is attained only for ``trivial'' reasons. Furthermore, there is an algorithm which, when given $ϕ$, calculates $λ(ϕ)$. | |
| dc.identifier | https://arxiv.org/abs/math/0504105 | |
| dc.identifier | http://arxiv.org/abs/math/0504105 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74806 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | 20F65 | |
| dc.title | The Subadditive Ergodic Theorem and generic stretching factors for free group automorphisms | |
| dc.type | text |