Yi Pan (IST Austria):
Reducibility of
quasi-periodic cocycles valued in symplectic groups
Abstract:
Reducibility of quasi-periodic cocyles valued in symplectic groups is
related to the spectrum of discrete Schrödinger operators on
strips. We will talk about a global reducibility result: given one
parameter families of such cocycles, for almost every one parameter,
either the maximal Lyapunov exponent is positive, or the cocycle is
almost reducible to some model. The techniques of the proof combine
Kotani thoery, KAM theory and study of hyperbolicity of renormalization
operator. This is a joint work with Artur Avila and Raphaël
Krikorian.