Abstract:

We will introduce dynamically compact systems as a new concept of chaotic dynamical systems, given by a compact metric space and a continuous surjective self-map. Observe that any weakly mixing system is transitive compact, and we show that any transitive compact M-system is weakly mixing. Then we will discuss the relationships among it and other several stronger forms of sensitivity. In particular, we will prove that any transitive compact system is Li-Yorke sensitive and furthermore multi-sensitive if it is not proximal.

Based on a joint work with Wen Huang, Danylo Khilko and Guohua Zhang.