Invariant measures for train track towers Auteur(s): Bedaride N., Hilion A., Lustig M.
Ref HAL: hal-01218333_v1 Ref Arxiv: 1503.08000 Ref. & Cit.: NASA ADS Exporter : BibTex | endNote Résumé: 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. |