2021/03/08 by Aihua Fan, Fan, Aihua, Shilei Fan +5
Mathematics · #37B40 #42A55 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals
paper · doi:10.48550/arxiv.2103.04745
openalex publication_date 2021/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the notion of Bohr chaoticity, which is a topological invariant for topological dynamical systems, and which is opposite to the property required by Sarnak's conjecture. We prove the Bohr chaoticity for all systems which have a horseshoe and for all toral affine dynamical systems of positive entropy, some of which don't have a horseshoe. But uniquely ergodic dynamical systems are not Bohr chaotic.