*Journées de Probabilités 2007*

**Tomasz Downarowicz **

*On various types of recurrence *

I will discuss the following general issue: let {*x, T(x), T*^{2}(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 *T*^{n}(x) belongs to *U*. How do the "largeness" properties of the sets *N(x,U)* relate to mixing properties of the system.

Slides