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1 results

Bohr chaoticity of principal algebraic actions and Riesz product measures
Part of
- Abstract harmonic analysis
- Ergodic theory
AI HUA FAN, KLAUS SCHMIDT, EVGENY VERBITSKIY
Journal:

Ergodic Theory and Dynamical Systems / Volume 44 / Issue 10 / October 2024

Published online by Cambridge University Press:

06 March 2024, pp. 2933-2959

Print publication:

October 2024
- Article
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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 actions of $\mathbb {Z}^d$ with positive entropy under the condition of existence of summable homoclinic points.