Colloquium: Tuesday, November 3, 2pm. Speaker: Benjamin Weiss (Hebrew University). Title: Affine dynamical systems.
An affine action by a group G is a continuous action of G on a compact convex K set by affine transformations. Such actions arise in a natural way whenever G acts by homeomorphisms of a compact topological space X by the action it induces on the set P(X) of probability measures on X. I will develop the basic properties of such actions and especially those of irreducible affine actions (an affine action is irreducible if it does not have any nontrivial invariant compact convex subsets of K). In particular I will explain why the action of SL_2(R)
(viewed as the group of Moebius transformations preserving the unit disk D) on P(S^1) is irreducible. Here S^1 is the boundary of the unit disk.
Based on joint work with Eli Glasner and Hillel Furstenberg.