Isaac Newton Institute for Mathematical Sciences

The Lyapunov exponent for certain ergodic matrix cocycles and the spectrum of the associated Schrödinger operator

Authors: Alexander Fedotov (Univ. St Petersburg), Frédéric Klopp (Univ. Paris 13)

Abstract

The aim of this work in progress is the study of the generalized eigenfuinctions associated to singular (in particular singular continuous) spectrum for a Schrödinger operator on the half-line. This study reduces to the study of an ergodic matrix cocycle for which we develop an exact renormalization analysis. In particular, we get a complete description of the set of ergodic parameters for which the Lyapunov exponent of the cocycle exists and does not exist.