Orbit Equivalence and Kakutani equivalence with Sturmian Subshifts

Pablo Dartnell, (1) , Fabien Durand (2) , Alejandro Maass (1, 3)

1 USACH - Universidad de Santiago de Chile [Santiago]
2 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352
3 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]

Using dimension group tools and Bratteli--Vershik representations of minimal Cantor systems we prove that a minimal Cantor system and a Sturmian subshift are topologically conjugate if and only if they are orbit equivalent and Kakutani equivalent.

Domaines: Systèmes dynamiques [math.DS]

Pablo Dartnell,, Fabien Durand, Alejandro Maass. Orbit Equivalence and Kakutani equivalence with Sturmian Subshifts. Studia Mathematica, 2000, 142 (1), pp.25-45. ⟨hal-01180295⟩