School of Mathematical Sciences
Monday, November 16, 2009
Schreiber 006, 12:15
Measure rigidity for dynamical systems
on (very) non-compact spaces
The long term statistical behavior of the orbits of a dynamical system T:X --> X can be studied by analyzing the invariant measures of T. Different measures correspond to different statistics of meandering in space. Usually, there are many different invariant measures, and listing all possible types of statistical behavior is intractable. But sometimes there are few invariant measures and this is possible. In such a case we speak of "measure rigidity".
There are many classical examples of measure rigidity where X is compact.The phenomenology is by now understood. But the situation in the non-compact case is not clear. I will survey some examples (mostly horocycle flows on infinite genus hyperbolic surfaces) which indicate the exotic phenomena which may appear in seriously non-compact situations.
Coffee will be served at 12:00 before the lecture
at Schreiber building 006