Distal dynamical systems, both in topological dynamics and ergodic theory, have had and continue to play an important role in the structure theory of dynamical systems and their applications to number theory. We will revisit the two relevant structure theorems by Furstenberg and Furstenberg-Zimmer on distal systems to underline this and then consider the question whether there is a closer connection than meets the eye between distal systems in ergodic theory on the one and distal systems in topological dynamics on the other hand. This will lead us to a result by Lindenstrauss which asserts that every distal ergodic system can be realized via a minimal distal topological system. We present a new and more general approach that makes this interplay between ergodic theory and topological dynamics more straight-forward (and incidentally, functorial). The foundation for this is given by a new operator-theoretic characterization of isometric extensions of topological dynamical systems which we develop based on an adaptation of Ellis' time-proven enveloping semigroups. Joint work with Henrik Kreidler (Wuppertal).

Meeting ID: 852 4277 3200 Passcode: 103121

You can see our past recorded seminars at https://www.youtube.com/channel/UClSidy-xXfs9roNj-rmAl2w/videos