ar X iv : 1 50 4 . 00 06 7 v 2 [ m at h . D S ] 8 J ul 2 01 7 EIGENVALUES OF MINIMAL CANTOR SYSTEMS
نویسندگان
چکیده
Abstract. 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.
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