Bohr chaoticity of topological dynamical systems

Authors：Fan, Aihua; Fan, Shilei^*; Ryzhikov, Valery V.; Shen, Weixiao

Source：Mathematische Zeitschrift, 2022, 302(2): 1127-1154.

DOI：10.1007/s00209-022-03093-6

We introduce the notion of Bohr chaoticity, which is a topological invariant for topological dynamical systems, and which means that the system is not orthogonal to any non-trivial weights. 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.

• Institution
  复旦大学