Andrés Navas: On cocycles of isometries and Lyapunov exponents

Although positive Lyapunov exponents are at the origin of "chaotic" dynamics, there are also dynamical systems with zero exponents exhibiting very complicated behavior which are far from being understood. In this  talk, I will consider the case of   linear cocycles. Using a classical technique coming from geometric group theory (namely, the "barycenter map" in spaces of nonpositive curvature), I will explain the ideas of proof of the following theorem (joint with J. Bochi): every linear cocycle with only zero exponents may be C0 approximated by a cocycle which is cohomologous to another cocycle taking values in a group of rotations (maximal compact group).