Continuity of the Lyapunov exponent for analytic quasiperiodic cocycles

Melinda Schulteis Concordia University, Irvine, USA

It is known that the Lyapunov exponent is not continuous at certain points in the space of continuous quasiperiodic cocycles. We show that it is continuous in the analytic category. Our applications include continuity of the Lyapunov exponent of quasiperiodic Jacobi matrices in various parameters. These results have important applications in the study of quantum dynamics. In particular, continuity of the Lyapunov exponent in energy is an important ingredient in the proof of dynamical localization for a family of operators of magnetic origin.