Seminar for Dynamic Systems

As part of the Seminar for Dynamic Systems, on Thursday, April 9th, 2026, 

at 4:00 p.m., in room 108 at the PMF-MO, Henk Bruin, Vienna University, will give a lecture entitled:

Ergodic properties of sums of visits to $[0,1/2)$ by quadratic irrational rotations.

Abstract: The visit sums and averages of orbits under irrational rotations has been of interest since at least the seminal work of Kesten in the 1960. Recent work by Avila et al. revisted the problem in the case that the rotation number is a quadratic irrational, showing that the typical behaviour is slightly different from what Kesten proved for typical rotation numbers. Their method is based on $\Z$-extension (skew-products) over the rotation and certain renormalization techniques. We recently generalized their method so as to include samples of Ehrenfest wind-tree model as well.

Using purely combinatoric methods, it is possible to give precise statements about visit sums for particular orbits, or actually the orbit of 0. This orbit is actually non-typical in view to the results of Avila et al.

The talk is based on joint work with Charles Fourgeron, Davide Ravotti, Dalia Terhesiu, and another with Robert Fokkink.