Invariant measures for train track towers - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2015

Invariant measures for train track towers

Arnaud Hilion
Martin Lustig
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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.
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Dates et versions

hal-01218333 , version 1 (21-10-2015)

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Nicolas Bedaride, Arnaud Hilion, Martin Lustig. Invariant measures for train track towers. 2015. ⟨hal-01218333⟩
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