Silvia Radinger (University of Vienna)
Abstract: In this talk we study measure-theoretical rigidity and partial rigidity for classes of Cantor dynamical systems including Toeplitz systems. The use of Bratteli-Vershik diagrams enables us to control the structure of the ergodic invariant measures.
Among other things, we will analyze different Toeplitz systems for their rigidity, show that there exist uniquely ergodic Toeplitz systems which have zero entropy and are not partially measure theoretically rigid and construct a Toeplitz system which has countably infinitely many ergodic invariant probability measures that are rigid with the same rigidity sequence. Further we show general conditions under which a Bratteli-Vershik system is rigid and give examples of non-rigidity.
This talk is based on joint work with Henk Bruin, Olena Karpel and Piotr Oprocha.