Zero-one laws for eventually always hitting points in mixing systems

Dmitry Kleinbock, Ioannis Konstantoulas, Florian Karl Richter

Published 2019-04-18Version 1

In this work we study the set of eventually always hitting points in shrinking target systems. These are points whose long orbit segments eventually hit the corresponding shrinking targets for all future times. Even in the presence of mixing, this set can behave erratically due to the involvement of extremal rather than mean statistics. For that reason, we focus our attention on systems where translates of targets exhibit near perfect mutual independence. For such systems we present tight conditions on the shrinking rate of the targets so that the set of eventually always hitting points is a null set (or co-null set respectively).