Dynamics of Cocycles and One-Dimensional Spectral Theory

Abstract

Many spectral questions about one-dimensional Schrödinger operators with quasi-periodic potentials can be reduced to dynamical questions about certain quasi-periodic SL(2, R)-valued cocycles. This connection has recently been employed to prove a number of long-standing conjectures. The aim of this mini-workshop was to bring together people from both spectral theory and dynamical systems in order to further develop and exploit the dynamical approach to quasi-periodic Schrödinger operators.

Localization via fractional moments for models on {\bb Z} with single-site potentials of finite support

“…However, due to the assumptions on the underlying probability space it seems that our model cannot be reduced to the ones in [17]. Avila and Damanik have related results as announced and sketched in [18,19].…”