A fundamental theme in Dynamics is the classification of systems up to appropriate equivalence relations. For this purpose, one seeks for dynamical invariants that are easy to compute and help to determine whether two systems can be equivalent to each other. In this research project we aim at finding and studying new invariants for particular classes of dynamical systems.

Given the the difficulty of classication, starting from the late 1990's so-called anti-classication results in Ergodic Theory have emerged. Using concepts from Descriptive Set Theory, they show in a rigorous way that classication for broad classes of measure-preserving dynamical systems is impossible. In this research project, we plan to address several new questions that arise from those results.

Please check out our project description for more information.