Journal of the European Mathematical Society, Volumen 21, Issue 3, 2019, Pages 727-775
Identifier
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14359855
Identifier
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10.4171/JEMS/849
Identifier
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https://repositorio.uchile.cl/handle/2250/171616
Abstract
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In this article we give necessary and sufficient conditions for a complex number 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 on the Bratteli–Vershik representations of such systems. As an application, from any minimal Cantor system, we construct a strong orbit equivalent system without irrational continuous 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.