Title: Spectrum of discrete quasiperiodic Schrodinger operators related dynamical properties
Speaker: Yi Pan（Université Paris Diderot-Paris 7）
Time: 16:00-17:00, August28
Location: Tecent Meeting, Tecent Meeting ID: 117 894 073
Abstract: Spectrum of discrete one-dimensional Schrodinger operators with dynamically defined potential, especially quasiperiodic one, is closely connected to uniform hyperbolicity of corresponding SL(2,R) cocycles. Moreover, the absolutely continuous spectrum is related to zeros of Lyapunov exponents and reducibility of cocycles while the pure point spectrum is related to nonuniformly hyperbolic behavior.
In this talk, we will give basic definition and explain this connection between spectrum and dynamical properties. Then we will focus on zero Lyapunov exponents and reducibility of cocycles. If time permitting, we will state a recent result on hyperbolicity of renormalization.
