Central Limit Theorems for the Shrinking Target Problem

International audienceSuppose B i := B(p, r i) are nested balls of radius r i about a point p in a dynamical system (T, X, µ). The question of whether T i x ∈ B i infinitely often (i. o.) for µ a.e. x is often called the shrinking target problem. In many dynamical settings it has been shown that if E n := n i=1 µ(B i) diverges then there is a quantitative rate of entry and lim n→