Eigenvalues of Toeplitz minimal systems of finite topological rank

Fabien Durand (1) , Alexander Frank (2, 3) , Alejandro Maass (2, 3)

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

In this article we characterize measure theoretical eigenvalues of Toeplitz Bratteli-Vershik minimal systems of finite topological rank which are not associated to a continuous eigenfunction. Several examples are provided to illustrate the different situations that can occur.

Domaines: Systèmes dynamiques [math.DS]

Fabien Durand, Alexander Frank, Alejandro Maass. Eigenvalues of Toeplitz minimal systems of finite topological rank. Ergodic Theory and Dynamical Systems, 2015, 30 p. ⟨10.1017/etds.2014.45⟩. ⟨hal-01180247⟩