Bohr chaoticity of principal algebraic actions and Riesz product measures

8 Mar 2021  ·  Aihua Fan, Klaus Schmidt, Evgeny Verbitskiy ·

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. read more

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Dynamical Systems 37B02, 42A55