Geometry, Topology and Dynamics Seminar
Julio Rebelo
University Paul-Sabatier Toulouse, France
On the regularity of stationary measures for non-discrete subgroups of Diff (S^1)
Abstract: Consider a (countable) subgroup $G$ of Diff (S^1) that is not discrete in the sense that it contains a non-trivial sequence of elements converging to the identity. The basic example of these groups is provided by a non-solvable finitely generated group $G$ admitting a generating set sufficiently close to the identity. Suppose in addition that $G$ possesses no finite orbit. A consequence of a theorem due to Deroin, Kleptsyn and Navas is that $G$ has a unique stationary measure $\mu$ on $S^1$ (for a fixed probability measure $\nu$ on $G$). In this talk we are going to shown that $\mu$ must be absolutely continuous with respect to the Lebesgue measure provided that $\nu$ is non-degenerate. As an application of it, we shall derive a rigidity result for measurable conjugacies between groups as above.
Wednesday December 2, 2009 at 3:00 PM in SEO 612