Eigenvalues of minimal Cantor systems

Fabien Durand, Alexander Frank, Alejandro Maass

Published 2015-04-01Version 1

In this article we provide necessary and sufficient conditions that a complex number should verify to be a measurable or a continuous eigenvalue of a minimal Cantor system. These conditions are established from the combinatorial information carried by the Bratteli-Vershik representations of such systems. Moreover we explore how modifications of the local order of these representations spoil the group of eigenvalues and their quality of being continuous or not. We show that, giving precise bounds, if there are not too many of these modifications then the group of continuous eigenvalues does not change for the resulting systems and too many could change this group significantly.