Michal Rams

Cocycles of circle diffeomorphisms

The (step one) cocycle of circle diffeomorphisms is a finite family of circle diffeomorphisms, which we are then allowed to apply in any order. Formally, it is a dynamical system on the space $S^1 \times \{1,\ldots,k\}^{\mathbb N}$ given by
\[
F(x,\omega) = (f_{\omega_1}, \sigma\omega).
\]
I’ll give an introduction to the multifractal theory of cocycles of circle diffeomorphisms, with applications to $SL(2,\mathbb R)$ matrix cocycles. The talk is based on several papers written with Lorenzo Diaz and Katrin Gelfert.