Nilpotent extensions of minimal group actions

Ulrich Haböck
(University of Vienna)

Abstract: I start with a short introduction on group extensions of dynamical systems and give few examples. Then I will focus on the dynamical behaviour of minimal systems extended by a non-abelian group $G$. The case $G$ being compact does not bear any difficulty (from the point of view of dynamics) but the situation becomes much more complicated considering non-compact extensions. Such extensions where only well understood when the group $G$ is abelian. However, it turns out that nilpotent extensions behave like abelian and it is also possible to generalise a regularity theorem to the nilpotent case. These results are from a joint work with Gernot Greschonig.