  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.
