Flexibility of measurable and topological nilfactors in dynamical systems
Abstract
We construct examples of minimal and uniquely ergodic systems realizing all possible behaviors in the interplay of measurable and topological nilfactors. To build such examples, we adapt an idea that stems from Furstenberg's construction of a minimal but not uniquely ergodic system on $\mathbb{T}^2$.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Advanced Topology and Set Theory
Holomorphic and Operator Theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 28 January 2026
- Document type
- Preprint