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Bohr chaoticity of principal algebraic actions and Riesz product measures
- Publication Year :
- 2021
-
Abstract
- For a continuous $\mathbb{N}^d$ or $\mathbb{Z}^d$ action on a compact space, we introduce the notion of Bohr chaoticity, which is an invariant of topological conjugacy and which is proved stronger than having positive entropy. We prove that all principal algebraic $\mathbb{Z}$ actions of positive entropy are Bohr-chaotic. The same is proved for principal algebraic $\mathbb{Z}^d$ ($d\ge 2$) actions of positive entropy under the condition of existence of summable homoclinic points.
- Subjects :
- Mathematics - Dynamical Systems
37B02, 42A55
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2103.04767
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1017/etds.2024.13