Analytic quasiperiodic matrix cocycles: continuity and quantization of the Lyapunov exponents
Seminar Room 1, Newton Institute
AbstractAs, beginning with the famous Hofstadter's butterfly, all numerical studies of spectral and dynamical quantities related to quasiperiodic operators are actually performed for their rational frequency approximants, the questions of continuity upon such approximation are of fundamental importance. The fact that continuity issues may be delicate is illustrated by the recently discovered discontinuity of the Lyapunov exponent for non-analytic potentials.
I will focus on work in progress, joint with Avila and Sadel, where we develop a new approach to continuity, powerful enough to handle matrices of any size and leading to a number of strong consequences.