A couple of days ago (on November 12th, 2014 to be more precise), Giovanni Forni gave a talk at the “flat seminar / séminaire plat” on the ergodicity of billiards on non-rational polygons, and, by following the suggestion of… 2,772 more words

## Tags » Ergodicity

#### A family of maps preserving the measure of ZxT

Last 15th October 2014, the “flat seminar” coorganized by Anton Zorich, Jean-Christophe Yoccoz and myself restarted in a new format: instead of one talk… 2,261 more words

#### Future Perfect – tales from the future – predictive analysis

In German-speaking countries, we can say “It will have been” because we have the Future Perfect tense. It appears that others envy us this possibility. In order to use the Future Perfect, you must think you know what is going to happen and you have to imagine what you would see looking back in time on the events for which the future has become the past. 1,245 more words

#### An abstract ergodic theorem, and the Mackey-Zimmer theorem

The von Neumann ergodic theorem (the Hilbert space version of the mean ergodic theorem) asserts that if is a unitary operator on a Hilbert space , and is a vector in that Hilbert space, then one has… 2,316 more words