Dynamical Systems Seminar

The classical multiplicative ergodic theorem (MET) for products of matrices is a major tool in smooth ergodic theory. Since Oseledet's original proof of the MET, various generalizations have appeared, notably to infinite dimensional settings of products of operators on Hilbert and Banach spaces, but these results make discreteness assumptions on the operators. Another line of work interprets the MET geometrically, viewing each matrix as acting isometrically on a non-positively curved space.

Without making any discreteness assumptions, we present how one of these geometric results, of Karlsson-Margulis, can be applied to get an MET for cocycles taking values in a finite von Neumann algebra.

This is joint work with Lewis Bowen and Ben Hayes.