64 citations · 197 across the 18 of their papers we have counts for
11 papers · 1 filter
Growth and order of automorphisms of free groups and free Burnside groups
Rémi Coulon, Arnaud Hilion
We prove that an outer automorphism of the free group is exponentially growing if and only if it induces an outer automorphism of infinite order of free Burnside groups with suffic…
Ergodic currents dual to a real tree
Thierry Coulbois, Arnaud Hilion
Let be an -tree in the boundary of Outer space with dense orbits. When the free group $\FN$ acts freely on , we prove that the number of projective classes of ergodic cu…
Botany of irreducible automorphisms of free groups
Thierry Coulbois, Arnaud Hilion
We give a classification of iwip outer automorphisms of the free group, by discussing the properties of their attracting and repelling trees.
Indecomposable -trees and minimal laminations
Thierry Coulbois, Arnaud Hilion, Patrick Reynolds
We extend the techniques of [CH] to build an inductive procedure for studying actions in the boundary of the Culler-Vogtmann Outer Space, the main novelty being an adaptation of he…
Free group automorphisms with parabolic boundary orbits
Arnaud Hilion
For , we show that there exist automorphisms of the free group which have a parabolic orbit in . In fact, we exhibit a technology for producing infinit…
Rips Induction: Index of the dual lamination of an -tree
Thierry Coulbois, Arnaud Hilion
Let be a -tree in the boundary of the Outer Space CV, with dense orbits. The -index of is defined by means of the dual lamination of . It is a generalisation…
-trees, dual laminations, and compact systems of partial isometries
Thierry Coulbois, Arnaud Hilion, Martin Lustig
Let $\FN$ be a free group of finite rank , and let be an -tree with a very small, minimal action of $\FN$ with dense orbits. For any basis $\CA$ of $\FN$ there ex…
Non-unique ergodicity, observers' topology and the dual algebraic lamination for -trees
Thierry Coulbois, Arnaud Hilion, Martin Lustig
We continue in this article the study of laminations dual to very small actions of a free group F on R-trees. We prove that this lamination determines completely the combinatorial…
-trees and laminations for free groups III: Currents and dual -tree metrics
Thierry Coulbois, Arnaud Hilion, Martin Lustig
This is the third of a series of three articles where we introduce laminations for the free-groups. We explore here the link between currents and laminations and prove that the sit…
-trees and laminations for free groups II: The dual lamination of an -tree
Thierry Coulbois, Arnaud Hilion, Martin Lustig
This is the second part of a series of three articles which introduce laminations for free groups (see math.GR/0609416 for the first part). Several definition of the dual laminatio…
-trees and laminations for free groups I: Algebraic laminations
Thierry Coulbois, Arnaud Hilion, Martin Lustig
This paper is the first of a sequence of three papers, where the concept of an -tree dual to a measured geodesic lamination in a hyperbolic surface is generalized to arb…