Tomas Persson: Non typical points

Abstract: I will talk about some recent results on non typical points in ergodic theory and diophantine approximation, that is points for which ergodic averages do not converge or points with non typical approximation properties. Sets of such points often belong to perticular classes of sets with large intersection properties, introduced by Falconer. These classes of sets have the properties that they are closed under countable intersections and consists of sets with large Hausdorff dimension. The talk is based on works by/with Färm, Reeve, Schmeling and myself.