Diophantine properties of dynamical systems and interval exchange
The lecture is based on a recent preprint with the same title, joint with
J. Chaika and put recently on arXiv. One of the results is that for
ergodic IETs (Interval Exchange Transformations) almost sure
The result is optimal in two ways:
(1) the normalizing factor $n$ cannot be improved, even for rotations;
(2) the assumption of ergodicity cannot be replaced by just minimality.
Several open problem (related) will be presented.