1. Schrödinger operators with potentials generated by hyperbolic transformations；2. Positivity of the Lyapunov exponent
报告人：David Damanik
报告地点：Zoom会议ID:941 567 2172
报告时间：2021年4月22日星期四09:00-09:50(part 1);10:00—11:10(part 2)
邀请人：李勇，冀书关，高忆先
报告摘要：
We discuss discrete one-dimensional Schrödinger operators whose potentials are generated by sampling along the orbits of a general hyperbolic transformation and present results showing that the Lyapunov exponent is positive away from a small exceptional set of energies for suitable choices of the ergodic measure and the sampling function. These results apply in particular to Schrödinger operators defined over expanding maps on the unit circle, hyperbolic automorphisms of a finite-dimensional torus, and Markov chains. (Joint work with Artur Avila and Zhenghe Zhang)
主讲人简介：
David Damanik, 美国Rice大学数学系Robert L. Moody冠名教授, Simons数学和理论物理研究员, J. Spectr. Theory杂志编辑, 主要从事动力系统和谱理论的研究, 在国际上最顶尖的四大综合性数学期刊Acta. Math., Ann. of Math., J. Amer. Math. Soc., Invent Math.上公开发表高质量学术论文8篇, 在Duke Math. J., Math, Ann., J. Eur. Math. Soc., J. Math. Pures Appl., Comm. Math. Phys.等国际权威期刊上公开发表高水平学术论文百余篇.
学校主页