Bohr chaoticity of topological dynamical systems
Dynamical Systems
2021-03-10 v2
Abstract
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.
Cite
@article{arxiv.2103.04745,
title = {Bohr chaoticity of topological dynamical systems},
author = {Aihua Fan and Shilei Fan and Valery Ryzhikov and Weixiao Shen},
journal= {arXiv preprint arXiv:2103.04745},
year = {2021}
}