Tuesday, August 9, 2022 - 11:15 in V3-204
Group actions with discrete spectrum and their amorphic complexity
A talk in the Mathematik in den Naturwissenschaften series by
Maik Gröger from Jagellonian University, Krakow
| Abstract: |
Amorphic complexity, originally introduced for integer actions, is a
topological invariant which measures the complexity of dynamical
systems in the regime of zero entropy. We will introduce its
definition for actions by locally compact sigma-compact amenable
groups on compact metric spaces. Further, we will illustrate some of
its basic properties and show why it is tailor-made to study strictly
ergodic group actions with discrete spectrum and continuous
eigenfunctions. This class of actions includes, in particular, Delone
dynamical systems related to regular model sets obtained via cut and
project schemes (CPS). Finally, for these kind of Delone dynamical
systems we present sharp upper bounds on amorphic complexity utilizing
basic properties of the corresponding CPS.
This is joint work with G. Fuhrmann, T. Jäger and D. Kwietniak.
Within the CRC this talk is associated to the project(s): A6 |
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