威尼斯人

报告题目：Reducibility and almost reducibility of quasi-periodic SL(2,R)-cocycles and applications (1)

报告人：赵之彦（法国Nice-Sophia Antipolis大学）

报告时间：2017年8月24日09:30-10：30

报告地点：维格堂319

报告摘要： In these talks, we will review some recent results on the reducibility and almost reducibility of quasi-periodic SL(2,R) cocycles. As an application, we estimate the size of spectral gaps of quasi-periodic Schrödinger operator. For the corresponding Schrödinger cocycle, we establish the quantitative reducibility at one edge point of the spectral gap. With an argument of Moser-Pöschel, we get another edge of the spectral gap by the variation of rotation number. Joint work with M. Leguil, J. You and Q. Zhou.

报告题目：Reducibility and almost reducibility of quasi-periodic SL(2,R)-cocycles and applications (2)

报告人：赵之彦（法国Nice-Sophia Antipolis大学）

报告摘要：By the upperbounds of the size of spectral gaps and the Hölder continuity of the integrated density of states, we can show the homogeneity of the spectrum of the corresponding Schrödinger operator. As a further corollary, we can show the almost periodicity in time for the solutions of the Toda lattice, if the initial condition is given by the quasi-periodic Schrödinger operator.

报告题目：Reducibility and almost reducibility of quasi-periodic SL(2,R)-cocycles and applications (3)

报告人：赵之彦（法国Nice-Sophia Antipolis大学）

报告摘要：As another application, we consider the time-dependent discrete one-dimensional quasi-periodic linear Schrödinger equation. We show that the equivalent H_1-norm grows linearly with respect to the time, in some cases where the corresponding linear Schrödinger operator has purely absolutely continuous spectrum. Joint work with Z. Zhang.