Distribution of polynomial orbits in Toeplitz systems
Abstract
Abstract We examine the convergence of ergodic averages along polynomials in Toeplitz systems and prove that it is possible for averages along one polynomial to converge, and along another to diverge. We also study the density of the polynomial orbits in Toeplitz systems—we show that it implies equidistribution of the polynomial orbits in the class of regular Toeplitz systems, but not in the class of strictly ergodic ones.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Quantum chaos and dynamical systems
Advanced Algebra and Geometry
Publication details
- Journal / source
- Ergodic Theory and Dynamical Systems
- Volume
- 46
- Issue
- 7
- Pages
- 1800–1818
- Publication date
- 26 February 2026
- Language
- EN