Dynamical Self-similar Covering Sets

Dynamical Self-similar Covering Sets

Sascha Troscheit, University of Oulu

A classical problem in dynamical systems is known as the shrinking target problem: given a sequence of 'target' subsets A_n \subset X and a dynamic T: X \to X we ask how 'large' the set of all points R \subset X is whose n-th iterate hits the target, T^n (x) \in A_n, infinitely often. Much progress has been made on understanding this type of 'recurrent' set and I will highlight some recent results on this and the related 'dynamical covering problem' which is a dynamical generalisation of the Dvoretzky covering problem. The talk is based on joint results with Balázs Bárány, and Henna Koivusalo and Balázs Bárány.

MC5417