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arXiv · 1711.05452

On the isomorphism problem for non-ergodic systems with discrete spectrum

Nikolai Edeko
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Abstract

The article presents a new perspective on the isomorphism problem for non-ergodic measure-preserving dynamical systems with discrete spectrum which is based on the connection between ergodic theory and topological dynamics constituted by topological models. By first solving the isomorphism problem for a certain class of topological dynamical systems, it is shown that the measure-preserving case can in fact be deduced from the topological one via the construction of topological models. As a byproduct, a new characterization of mean ergodicity for topological dynamical systems is obtained.

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Nikolai Edeko. 2018-01-05. On the isomorphism problem for non-ergodic systems with discrete spectrum. https://arxiv.org/abs/1711.05452

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