A note on Bohr chaos and hyperbolic sets

Abstract

This paper studies the relationship between shadowing phenomena and Bohr chaos in dynamical systems. We provide sufficient conditions for Bohr chaos in terms of shadowing. By combining those conditions with the shadowing lemma, we obtain some results on Bohr chaos and hyperbolic sets. Our results also highlight some simple but non-trivial structural properties of hyperbolic sets.

arXiv comment13 pages, minor corrections made, Appendices A, B added