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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On Lyapunov exponents of continuous Schrödinger cocycles over irrational rotations


Authors: Wen Huang and Yingfei Yi
Journal: Proc. Amer. Math. Soc. 140 (2012), 1957-1962
MSC (2010): Primary 37B55; Secondary 37D25
Published electronically: September 26, 2011
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Abstract: In this paper we consider continuous, SL$ (2,\mathbb{R})$-valued, Schrödinger cocycles over irrational rotations. We prove two generic results on the Lyapunov exponents which improve the corresponding ones contained in a paper by Bjerklöv, Damanik and Johnson.


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Additional Information

Wen Huang
Affiliation: Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences, Hefei Anhui 230026, People’s Republic of China
Email: wenh@mail.ustc.edu.cn

Yingfei Yi
Affiliation: School of Mathematics, Jilin University, Changchun, 130012, People’s Republic of China – and – School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
Email: yi@math.gatech.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11042-6
PII: S 0002-9939(2011)11042-6
Keywords: Lyapunov exponent, Schrödinger cocycles, non-uniform hyperbolicity
Received by editor(s): December 5, 2010
Received by editor(s) in revised form: January 30, 2011
Published electronically: September 26, 2011
Additional Notes: The first author is partially supported by NSFC(10911120388,11071231), Fok Ying Tung Education Foundation and the Fundamental Research Funds for the Central Universities (WK0010000001,WK0010000014).
The second author is partially supported by NSF grant DMS0708331, NSFC Grant 10428101, and a Changjiang Scholarship from Jilin University
Communicated by: Bryna Kra
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.