Topological dynamics of irregular model sets

Abstract: Model sets have been introduced by Yves Meyer in 1972. As the underlying cut and project schemes present a quite general method to construct aperiodic point-sets with long-range order, they are often studied in the theory of mathematical quasicrystals. At the same time, they present an interesting class of examples in the context of topological dynamics.

In this talk, we will concentrate on the dynamics of so-called irregular model sets, whose dynamics are generally more complicated and less understood than that of regular models (like the Fibonacci quasicrystal). We show that the Delone dynamical systems associated to irregular model sets often show positive entropy, but the construction also allows for uniquely ergodic zero entropy examples. However, irregular models sets cannot be tame, which provides a lower bound for the complexity of their dynamics.

dynamical systems

Audience: researchers in the topic

Dynamical systems seminar at the Jagiellonian University