On the isomorphism problem for non-ergodic systems with discrete spectrum
arXiv:1711.05452
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.
arXiv commentA paper by Kwiatkowski was kindly brought to my attention by Xiangdong Ye and has now been taken into account