Title: Genericity in Topological Dynamics
Speaker: Michael Hochman
Speaker Info: Hebrew University
Special Note: Unusual Time
I'll describe some results on the genericity of dynamical properties in the homeomorphism group of the Cantor set. For this purpose, the most interesting space to consider is the Polish subspace of totally transitive systems. Here the picture we see is surprisingly different from the analogue in ergodic theory. For instance, both strong mixing and minimal self joinings are generic.Date: Friday, January 12, 2007
These results were obtained using symbolic techniques which can be applied by transferring the question to a different setting, namely, the space of closed invariant subspaces of a suitable shift space. I'll explain this transfer, which is an analogue of a similar known phenomenon in ergodic theory.