On the Spectrum and Lyapunov Exponent of Limit Periodic Schrödinger Operators

被引：0
|
作者：
Artur Avila
机构：
[1] Université Pierre et Marie Curie–Boîte Courrier 188,CNRS UMR 7599, Laboratoire de Probabilités et Modèles Aléatoires
[2] IMPA,undefined
来源：
Communications in Mathematical Physics | 2009年 / 288卷
关键词：
Hull; Lebesgue Measure; Lyapunov Exponent; Spectral Radius; Cantor Group;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We exhibit a dense set of limit periodic potentials for which the corresponding one-dimensional Schrödinger operator has a positive Lyapunov exponent for all energies and a spectrum of zero Lebesgue measure. No example with those properties was previously known, even in the larger class of ergodic potentials. We also conclude that the generic limit periodic potential has a spectrum of zero Lebesgue measure.
引用
收藏
页码：907 / 918
页数：11
相关论文
共 50 条
12345