Dynamical Systems Seminar

This is joint work with T. Jager and C. Liu. We study the multivariate notions of diam-mean m-equicontinuity and the corresponding dual notion of diam-mean m-sensitivity for m>1. To formalise this duality, we establish an Auslander-Yorke type dichotomy: every minimal system is either diam-mean m-equicontinuous or diam-mean m-sensitive. The main focus of the talk is a local characterisation of multivariate mean sensitivity in terms of weakly mean sensitive tuples. We show that, in transitive systems, diam-mean m-sensitivity is equivalent to the existence of an essential weakly mean sensitive m-tuple, thereby providing a local description of this global dynamical property.