Lyapunov exponents of continuous Schrodinger cocycles over irrational rotations

被引:3
作者
Bjerkloev, Kristian [1 ]
Damanik, David
Johnson, Russell
机构
[1] Univ Toronto, Dept Math, Toronto, ON M5S 1A1, Canada
[2] CALTECH, Dept Math, Pasadena, CA 91125 USA
[3] Univ Florence, Dipartimento Sistemi & Informat, I-50139 Florence, Italy
关键词
D O I
10.1007/s10231-006-0029-7
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider the Lyapunov exponent of those continuous SL( 2, R)-valued cocycles over irrational rotations that appear in the study of Schrodinger operators and prove generic results related to large coupling asymptotics and uniform convergence.
引用
收藏
页码:1 / 6
页数:6
相关论文
共 17 条
[1]   Generic singular spectrum for ergodic Schrodinger operators [J].
Avila, A ;
Damanik, D .
DUKE MATHEMATICAL JOURNAL, 2005, 130 (02) :393-400
[2]   Positive Lyapunov exponent and minimality for a class of one-dimensional quasi-periodic Schrodinger equations [J].
Bjerklöv, K .
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2005, 25 :1015-1045
[3]   The Lyapunov exponents of generic volume-preserving and symplectic maps [J].
Bochi, J ;
Viana, M .
ANNALS OF MATHEMATICS, 2005, 161 (03) :1423-1485
[4]   Genericity of zero Lyapunov exponents [J].
Bochi, J .
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2002, 22 :1667-1696
[5]   On nonperturbative localization with quasi-periodic potential [J].
Bourgain, J ;
Goldstein, M .
ANNALS OF MATHEMATICS, 2000, 152 (03) :835-879
[6]   Zero-measure Cantor spectrum for Schrodinger operators with low-complexity potentials [J].
Damanik, David ;
Lenz, Daniel .
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2006, 85 (05) :671-686
[7]   A condition of Boshernitzan and uniform convergence in the multiplicative ergodic theorem [J].
Damanik, David ;
Lenz, Daniel .
DUKE MATHEMATICAL JOURNAL, 2006, 133 (01) :95-123
[8]  
Fabbri R, 2002, BOLL UNIONE MAT ITAL, V5B, P149
[9]  
Fabbri R., 1999, DIFF EQNS DYNAM SYS, V7, P349
[10]   Holder continuity of the integrated density of states for quasi-periodic Schrodinger equations and averages of shifts of subharmonic functions [J].
Goldstein, M ;
Schlag, W .
ANNALS OF MATHEMATICS, 2001, 154 (01) :155-203