On orthogonality to uniquely ergodic systems
Dynamical Systems
2025-02-06 v3
Abstract
We solve Boshernitzan's problem of characterization (in terms of so called Furstenberg systems) of bounded sequences that are orthogonal to all uniquely ergodic systems. Some variations of Boshernitzan's problem involving characteristic classes are considered. As an application, we characterize sequences orthogonal to all uniquely ergodic systems whose (unique) invariant measure yields a discrete spectrum automorphism as those satisfying an averaged Chowla property.
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Cite
@article{arxiv.2404.07907,
title = {On orthogonality to uniquely ergodic systems},
author = {Martyna Górska and Mariusz Lemańczyk and Thierry de la Rue},
journal= {arXiv preprint arXiv:2404.07907},
year = {2025}
}
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