A RANDOM COCYCLE WITH NON HOLDER LYAPUNOV EXPONENT

被引：9

作者：

Duarte, Pedro ^{[1
,2
]}

Klein, Silvius ^{[3
]}

Santos, Manuel ^{[4
]}

机构：

[1] Univ Lisbon, Fac Ciencias, Dept Matemat, Edificio C6,Piso 2, P-1749016 Lisbon, Portugal

[2] Univ Lisbon, Fac Ciencias, CMAFCIO, Edificio C6,Piso 2, P-1749016 Lisbon, Portugal

[3] Pontificia Univ Catolica Rio De Janeiro PUC Rio, Dept Matemat, Rua Marques Sao Vicente 225, BR-22430060 Rio De Janeiro, RJ, Brazil

[4] Univ Lisbon, Inst Super Tecn, Dept Matemat, Ave Rovisco Pais, P-1049001 Lisbon, Portugal

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2019年 / 39卷 / 08期

关键词：

Random linear cocycle; Lyapunov exponent; discrete Schrodinger operator; integrated density of states; Thouless formula; INTEGRATED DENSITY; CONTINUITY; STATES; DISCRETE; PRODUCTS;

D O I：

10.3934/dcds.2019197

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide an example of a Schrodinger cocycle over a mixing Markov shift for which the integrated density of states has a very weak modulus of continuity, close to the log-Holder lower bound established by W. Craig and B. Simon in [6]. This model is based upon a classical example due to Y. Kifer [15] of a random Bernoulli cocycle with zero Lyapunov exponents which is not strongly irreducible. It follows that the Lyapunov exponent of a Bernoulli cocycle near this Kifer example cannot be Holder or weak-Holder continuous, thus providing a limitation on the modulus of continuity of the Lyapunov exponent of random cocycles.

引用

页码：4841 / 4861

页数：21

共 24 条

[1]

[Anonymous], 2012, GRADUATE STUDIES MAT, DOI DOI 10.1090/GSM/132.MR2906465

[2]

Avila A., ABOMINABLE PRO UNPUB

[3] On the Spectrum and Lyapunov Exponent of Limit Periodic Schrodinger Operators [J].