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The Lyapunov exponent for certain ergodic matrix cocycles and the spectrum of the associated Schr\"{o}dinger operator

Klopp, F (Universite de Paris Nod)
Monday 24 July 2006, 10:00-10:50

Seminar Room 1, Newton Institute


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.


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