Abstract:

In this seminar we focus on the ergodic and entropy theory on the hereditary shift which is introduced by Kerr-Li (Math. Ann. 2007). Hereditary shift generalizes many important subshifts, e.g., spacing and beta shifts. The topological behavior (e.g., specification properties, recurrence theory) and the entropy theory are very important topics and are worth to investigate. We will give the up-to-date survey of entropy theory on hereditary shifts and the specification properties on spacing shifts. Some open problems of the hereditary shifts will also be listed in this seminar.