Paul E. Schupp

most citedThe Subadditive Ergodic Theorem and generic stretching factors for free group automorphisms

3 citations · 3 across the 2 of their papers we have counts for

collaborators

2 papers

math.GR2005

Densities in free groups and $Z^{k}$ , Visible Points and Test Elements

Ilya Kapovich, Igor Rivin, Paul Schupp +1

In this article we relate two different densities. Let $F_{k}$ be the free group of finite rank $k \geq 2$ and let $α$ be the abelianization map from $F_{k}$ onto $Z^{k}$ . We pr…

math.GR2005★ 3 cited

The Subadditive Ergodic Theorem and generic stretching factors for free group automorphisms

Vadim Kaimanovich, Ilya Kapovich, Paul Schupp

Given a free group $F_{k}$ of rank $k \geq 2$ 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 gener…

Densities in free groups and Zk, Visible Points and Test Elements

The Subadditive Ergodic Theorem and generic stretching factors for free group automorphisms

Densities in free groups and $Z^{k}$ , Visible Points and Test Elements