64 citations · 197 across the 18 of their papers we have counts for
20 papers
Measure transfer and -adic developments for subshifts
Nicolas Bédaride, Arnaud Hilion, Martin Lustig
Based on previous work of the authors, to any -adic development of a subshift a "directive sequence" of commutative diagrams is associated, which consists at every level $n…
The measure transfer for subshifts induced by a morphism of free monoids
Nicolas Bédaride, Arnaud Hilion, Martin Lustig
Every non-erasing monoid morphism induces a {\em measure transfer map} between the me…
Invariant measures on finite rank subshifts
Nicolas Bédaride, Arnaud Hilion, Martin Lustig
In this note we show that for any subshift of finite -rank every invariant measure is determined by its values on finitely many cylinders. Under mild conditions these cy…
Tower power for -adics
Nicolas Bédaride, Arnaud Hilion, Martin Lustig
We explain and restate the results from our recent paper arXiv:1503.08000.v3 in standard language for substitutions and -adic systems in symbolic dynamics. We then produce as ra…
The visual boundary of hyperbolic free-by-cyclic groups
Yael Algom-Kfir, Arnaud Hilion, Emily Stark
Let be an atoroidal outer automorphism of the free group . We study the Gromov boundary of the hyperbolic group . We explicitly describe a…
Topological substitutions and Rauzy fractals
Nicolas Bédaride, Arnaud Hilion, Timo Jolivet
We consider two families of planar self-similar tilings of different nature: the tilings consisting of translated copies of the fractal sets defined by an iterated function system,…
Graph towers, laminations and their invariant measures
Nicolas Bédaride, Arnaud Hilion, Martin Lustig
In this paper we present a combinatorial machinery, consisting of a graph tower and vector towers on , which allows us to ef…
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…
The hyperbolicity of the sphere complex via surgery paths
Arnaud Hilion, Camille Horbez
Handel and Mosher have proved that the free splitting complex FS for the free group is Gromov hyperbolic. This is a deep and much sought-after result, since it establishes FS as a…
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…
Geometric realizations of two dimensional substitutive tilings
Nicolas Bedaride, Arnaud Hilion
We define 2-dimensional topological substitutions. A tiling of the Euclidean plane, or of the hyperbolic plane, is substitutive if the underlying 2-complex can be obtained by itera…
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…