Necessary and sufficient conditions to be an eigenvalue for linearly recurrent dynamical Cantor systems

Xavier Bressaud , Fabien Durand (1) , Alejandro Maass (2)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée
2 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]

We give necessary and sufficient conditions to have measurable and continuous eigenfunctions for linearly recurrent Cantor dynamical systems. We also construct explicitly an example of linearly recurrent system with nontrivial Kronecker factor and a trivial maximal equicontinuous factor.

Mots clés: linearly recurrent; eigenvalues

Domaines: Systèmes dynamiques [math.DS]

Xavier Bressaud, Fabien Durand, Alejandro Maass. Necessary and sufficient conditions to be an eigenvalue for linearly recurrent dynamical Cantor systems. Journal of the London Mathematical Society, 2005, 72 (3), pp.799-816. ⟨hal-00224277⟩