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Eigenvalues of minimal Cantor systems by Durand, Fabien; Frank, Alexander; Maass, Alejandro is a scholarly article available to read on EtoBox.

What is Eigenvalues of minimal Cantor systems about?

In this article we give necessary and sufficient conditions that a complex number must satisfy to be a continuous eigenvalue of a minimal Cantor system. Similarly, for minimal Cantor systems of finite rank, we provide necessary and sufficient conditions for having a measure theoretical eigenvalue. These conditions are established from the combinatorial information of the Bratteli-Vershik representations of such systems. As an application, from any minimal Cantor system, we construct a strong orbit equivalent system without irrational eigenvalues which shares all measure theoretical eigenvalues with the original system. In a second application a minimal Cantor system is constructed satisfying the so-called maximal continuous eigenvalue group property.

Author

Durand, Fabien; Frank, Alexander; Maass, Alejandro

Published

2015

Language

EN