Speaker：Aihua Fan (Université de Picardie Jules Verne)

Time：2024-5-7, 16:00

Location：Conference Room 686 at the 6th floor of Shuli Building at Haiyun Campus 

Abstract:

The Bohr chaoticity is a complexity of a dynamical system and is a topological invariant; it implies the positivity of entropy. However, the positivity of entropy doesn’t imply the Bohr chaoticity. We prove that a system (X, T) admitting a horseshoe (i.e a susbsytem of some power of T is conjugate to a full shift) is Bohr chaotic. Thus the usual nice systems of positive entropy are Bohr chaotic. But systems having few ergodic measures are not Bohr chaotic.  Another class of systems which are proved to be Bohr chaotic are the algebraic principal systems.  These are joint works with Shilei FAN (Wuhan), Valery RYZHYKOV (Moscou), Klaus SCHMIDT (Vienna), Weixiao SHEN (Shanghai) and Evgeny VERBITSKIY (Leiden). Some related questions will be discussed.