Modul: MAT760 Ergodic Theory and Dynamical Systems Seminar

## Some remarks on the `eventually always hitting' property

Talk by Prof. Dr. Dmitry Kleinbock

**Date:** 03.05.21 **Time:** 15.00 - 16.15 **Room:** ETH HG G 19.2

Eventually always hitting (EAH) points are those whose long orbit segments eventually hit the corresponding shrinking targets for all future times. This is a uniform version of the classical hitting property in ergodic theory with shrinking targets; the terminology is due to Dubi Kelmer. Unlike its classical counterpart, not much is known about conditions on the targets for which almost all vs. almost no points are EAH. I will talk about systems where translates of targets exhibit near perfect mutual independence, such as Bernoulli schemes. For such systems tight conditions on the shrinking rate of the targets can be stated so that the set of eventually always hitting points is null or co-null. This is a joint work with Ioannis Konstantoulas and Florian Richter.