Bohr chaoticity of topological dynamical systems

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.