On orthogonality to uniquely ergodic systems
Abstract
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. As a step toward this solution, we provide a characterization of automorphisms which are disjoint from all ergodic ones as those whose a.a. ergodic components form a family of pairwise disjoint automorphisms. 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.
Fields of Study & Subjects
Advanced Scientific Research Methods
Mathematical Control Systems and Analysis
advanced mathematical theories
Publication details
- Journal / source
- Journal d Analyse Mathématique
- Publisher
- Springer Science and Business Media LLC
- Volume
- 159
- Issue
- 2
- Pages
- 581–674
- Publication date
- 19 July 2026
- Language
- EN