Symbolic discrepancy and Pisot dynamics

Vortrag von Prof. Dr. Valérie Berthé

Datum: 06.12.21  Zeit: 15.00 - 16.00  Raum:

Discrepancy is a measure of equidistribution for sequences of points. A bounded remainder set is a set with bounded discrepancy, that is, the number of times it is visited differs by the expected time only by a constant. We discuss dynamical, symbolic and spectral approaches to the study of bounded remainder sets for Kronecker sequences. We also consider discrepancy in the setting of symbolic dynamics and we discuss the existence of bounded remainder sets for some families of zero entropy subshifts. We focus on the case of Pisot parameters for toral translations and then show how to construct symbolic codings in terms of multidimensional continued fraction algorithms which lead to renormalization schemes. This is joint work with W. Steiner and J. Thuswaldner.