4 citations · 8 across the 12 of their papers we have counts for
20 papers
Densities in free groups and , Visible Points and Test Elements
Ilya Kapovich, Igor Rivin, Paul Schupp +1
In this article we relate two different densities. Let be the free group of finite rank and let be the abelianization map from onto . We pr…
The Subadditive Ergodic Theorem and generic stretching factors for free group automorphisms
Vadim Kaimanovich, Ilya Kapovich, Paul Schupp
Given a free group of rank with a fixed set of free generators we associate to any homomorphism from to a group with a left-invariant semi-norm a gener…
Currents on free groups
Ilya Kapovich
We study the properties of geodesic currents on free groups, particularly the "intersection form" that is similar to Bonahon's notion of the intersection number between geodesic cu…
Translation equivalence in free groups
Ilya Kapovich, Gilbert Levitt, Paul Schupp +1
Motivated by the work of Leininger on hyperbolic equivalence of homotopy classes of closed curves on surfaces, we investigate a similar phenomenon for free groups. Namely, we study…
The frequency space of a free group
Ilya Kapovich
We analyze the structure of the \emph{frequency space} of a nonabelian free group consisting of all shift-invariant Borel probability measures on $\partia…
Delzant's T-invariant, Kolmogorov complexity and one-relator groups
Ilya Kapovich, Paul Schupp
We prove that ``almost generically'' for a one-relator group Delzant's -invariant (which measures the smallest size of a finite presentation for a group) is comparable in magnit…