DAAD funds joint project with the Jagiellonian University Krakow

The two-year project aims to contribute to the understanding and quantification of the dynamical complexity of time-dependent systems. A central notion in this context is entropy, which allows to measure
the ‘chaoticity’ inherent in a system. However, even zero-entropy systems still show a remarkable variety
of dynamical behaviours and their study has been an active field of research over the last decades. A particular motivation comes from the theory of aperiodic order, where mathematical models of quasicrystals, such as the Penrose tiling or substitution systems, induce associated topological dynamical systems. Different degrees of long-range order then correspond to different levels of dynamical complexity. An alternative viewpoint for the classification of dynamical systems is to study their extension structures. This approach led to seminal results such as the Furstenberg, Furstenberg-Zimmer and Veech Structure Theorems.

The goal of the research programme is to combine both these approaches and to investigate topological dynamical systems of zero entropy by means of new topological invariants and from the viewpoint of extension structures. Thereby, the project builds on long-standing and fruitful collaborations between the two resarch groups and will help to intensify these ties. It involves several young scientists on both sides, whose support is at the heart of the programme.