Set of invariant measures of generalized Toeplitz subshifts

María Isabel Cortez (1) , Samuel Petite (2)

1 DMCC - Departamento de Matemática y Ciencia de la Computación [Santiago de Chile]
2 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

We show that for every metrizable Choquet simplex $K$ and for every group $G$, which is amenable, finitely generated and residually finite, there exists a Toeplitz $G$-subshift whose set of shift-invariant probability measures is affine homeomorphic to $K$. Furthermore, we get that for every integer $d\geq 1$ and every minimal Cantor system $(X,T)$ whose dimension group is divisible, there exists a minimal Toeplitz ${\mathbb Z}^d$-subshift which is topologically orbit equivalent to $(X,T)$.

Mots clés: Toeplitz subshift; discrete group actions; invariant measures; orbit equivalence; orbit equivalence.

Domaines: Systèmes dynamiques [math.DS]

María Isabel Cortez, Samuel Petite. Set of invariant measures of generalized Toeplitz subshifts. Groups, Geometry, and Dynamics, 2016, 8 (4), pp.1007-1047. ⟨hal-00602238⟩