A note on Lyapunov exponents of deterministic strongly mixing potentials

被引：4
|
作者：
Bourgain, Jean [1 ]
Bourgain-Chang, Eric [2 ]
机构：
[1] Inst Adv Study, Princeton, NJ 08540 USA
[2] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA
来源：
JOURNAL OF SPECTRAL THEORY | 2015年 / 5卷 / 01期
关键词：
Lyapounov exponent; Schrodinger operator; transfer matrix;
D O I：
10.4171/JST/89
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this Note, we consider 1D lattice Schrodinger operators with deterministic strongly mixing potentials as studied in [3] and [2] with very small coupling. We describe a scheme to establish positivity of the Lyapunov exponent from a statement at some fixed scale. The required input may then be derived from Furstenberg theory, if the underlying dynamics are sufficiently mixing, or verified directly by numerical means.
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页码：1 / 15
页数：15
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