47 citations · 349 across the 75 of their papers we have counts for
5 papers · 1 filter
The primitivity index function for a free group, and untangling closed curves on hyperbolic surfaces. With an appendix by Khalid Bou-Rabee
Neha Gupta, Ilya Kapovich
Motivated by the results of Scott and Patel about "untangling" closed geodesics in finite covers of hyperbolic surfaces, we introduce and study primitivity, simplicity and non-fill…
A train track directed random walk on
Ilya Kapovich, Catherine Pfaff
Several known results, by Rivin, Calegari-Maher and Sisto, show that an element , obtained after steps of a simple random walk on , is fully irreduci…
Patterson-Sullivan currents, generic stretching factors and the asymmetric Lipschitz metric for Outer space
Ilya Kapovich, Martin Lustig
We quantitatively relate the Patterson-Sullivant currents and generic stretching factors for free group automorphisms to the asymmetric Lipschitz metric on Outer space and to Guira…
Unbounded asymmetry of stretch factors
Spencer Dowdall, Ilya Kapovich, Christopher J Leininger
A result of Handel-Mosher guarantees that the ratio of logarithms of stretch factors of any fully irreducible automorphism of the free group and its inverse is bounded by a c…
Conical limit points and the Cannon-Thurston map
Woojin Jeon, Ilya Kapovich, Christopher Leininger +1
Let be a non-elementary word-hyperbolic group acting as a convergence group on a compact metrizable space so that there exists a continuous -equivariant map $i:\partial…