Reducibility of quasi-periodic cocycles valued in symplectic groups

Speaker. Yi Pan
Date. 31.01.23 at 3:30 pm

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 in real analytic category: given one parameter families of such cocycles, for almost every parameter, either the maximal Lyapunov exponent is positive, or the cocycle is almost reducible to some model. The techniques of the proof combine Kotani theory, KAM theory and in particular study of hyperbolicity of renormalization operator. This is a joint work with Artur Avila and Raphaël Krikorian.