Shrinking target problem on Bedford-McMullen carpets

Given a dynamical system $(X,T)$ and a decreasing family of open sets $U_n$ one defines the shrinking target set as the set of points $x\in X$ such that $T^nx \in U_n$ for infinitely many $n$'s. In this talk I will describe the shrinking target set for an affine expanding map on the plane corresonding to the Bedford-McMullen affine iterated function systems. It is a joint work with Balazs Barany from Budapest Technical University.