%0 Unpublished work
%T Invariant measures for train track towers
%+ Institut de Mathématiques de Marseille (I2M)
%A Bedaride, Nicolas
%A Hilion, Arnaud
%A Lustig, Martin
%8 2015-10-21
%D 2015
%Z 1503.08000
%Z Mathematics [math]/Dynamical Systems [math.DS]
%Z Mathematics [math]/Group Theory [math.GR]Preprints, Working Papers, ...
%X In this paper we present a combinatorial machinery, consisting of a graph tower Γ← and a weight towers ω← on Γ←, which allow us to efficiently describe invariant measures μ=μω← on rather general discrete dynamicals system over a finite alphabet. A train track map f:Γ→Γ defines canonically a stationary such graph tower Γf←. In the most important two special cases the measure μ specializes to a (typically ergodic) invariant measure on a substitution subshift, or to a projectively f∗-invariant current on the free group π1Γ. Our main result establishes a 1-1 correspondence between such measures μ and the non-negative eigenvectors of the incidence ("transition") matrix of f.
%G English
%2 https://hal.science/hal-01218333/document
%2 https://hal.science/hal-01218333/file/1503.08000v2.pdf
%L hal-01218333
%U https://hal.science/hal-01218333
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ I2M
%~ I2M-2014-
%~ TDS-MACS