Journées de Probabilités 2007

Tomasz Downarowicz

On various types of recurrence

I will discuss the following general issue: let {x, T(x), T2(x),...} be a trajectory of a point x in a dynamical system and let U be a set of positive measure (or an open set) containing x. Let N(x,U) be the set of times n such that Tn(x) belongs to U. How do the "largeness" properties of the sets N(x,U) relate to mixing properties of the system.