
Abstract: In this talk we will give an overview of variety topological dynamics concept in the setting of separable Banach Space. These notions include toplogical mixing, transitvity, Li-Yorke chaos, Devaney chaos as well as measures which are transformation invariant. In addition, we will discuss some results coauthored by the speaker and some open problems. All concepts will be defined and talk will be accessible to graduate students and non specialists.