Ergodic theorems for actions of large groups
Supervisor: Alexander Gorodnik
Let us consider a space X equipped with a measure and an action of the group G which preserves the measure. While the elements of G act chaotically and the structure of the orbits is very complicated, we still would like to make some statistical predictions regarding their behaviour. One of the fundamental problems in ergodic theory is to describe the asymptotic distribution of typical orbits. Classically, this problem was investigated for one-parameter groups, and it is crucial for many applications to understand the distribution of orbits for actions of general groups.
1. V. Bergelson and A. Gorodnik, Trieste lectures on ergodic theorems and applications, http://www.maths.bris.ac.uk/~mazag/papers/lectures.pdf
2. A. Nevo, Pointwise ergodic theorems for actions of groups. Handbook of dynamical systems. Vol. 1B, 871-982, Elsevier B. V., Amsterdam, 2006.
3. Theoremes ergodiques pour les actions de groupes, http://fdpoisson.org/doc/LivreMB.pdf