Modul:   MAT760  Ergodic theory and dynamical systems seminar

Reducibility of quasi-periodic cocycles valued in symplectic groups

Talk by Dr. Yi Pan

Speaker invited by: Prof. Dr. Artur Avila

Date: 20.03.24  Time: 13.30 - 14.30  Room: ETH HG G 19.1

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 family of such cocycles, for almost every parameter, either the maximal Lyapunov exponent is positive, or the cocycle is almost conjugate to some precise model. The techniques include Kotani thoery, KAM theory and in particular study of hyperbolicity of renormalization operator. This is a joint work with Artur Avila and Raphaël Krikorian.