On the isomorphism problem for non-minimal transformations with discrete spectrum

Nikolai Edeko

doi:10.3934/dcds.2019262

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2019, Volume 39, Issue 10: 6001-6021. Doi: 10.3934/dcds.2019262

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On the isomorphism problem for non-minimal transformations with discrete spectrum

Nikolai Edeko

Mathematisches Institut, Universität Tübingen, Auf der Morgenstelle 10, D-72076 Tübingen, Germany

Received: November 30, 2018

Revised: April 30, 2019

Published: July 2019

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Abstract

The article addresses the isomorphism problem for non-minimal topological dynamical systems with discrete spectrum, giving a solution under appropriate topological constraints. Moreover, it is shown that trivial systems, group rotations and their products, up to factors, make up all systems with discrete spectrum. These results are then translated into corresponding results for non-ergodic measure-preserving systems with discrete spectrum.

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Mathematics Subject Classification: Primary: 37A05, 37B05.

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