Quantitative reducibility of Gevrey quasi-periodic cocycles and its applications

被引:0
|
作者
Li, Xianzhe [1 ,2 ]
机构
[1] Nankai Univ, Chern Inst Math, Tianjin 300071, Peoples R China
[2] Nankai Univ, LPMC, Tianjin 300071, Peoples R China
基金
国家重点研发计划;
关键词
Gevrey class; long range operator; pure point spectrum; interval spectrum; reducibility theory; spectral gap; SCHRODINGER-OPERATORS; ROTATION NUMBER; HOLDER CONTINUITY; LYAPUNOV EXPONENT; LOCALIZATION; SPECTRUM;
D O I
10.1088/1361-6544/ac98ed
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We establish a quantitative version of strong almost reducibility result for SL(2, R) quasi-periodic cocycle close to a constant in the Gevrey class. We prove that, if the frequency is Diophantine, the long range operator has pure point spectrum with sub-exponentially decaying eigenfunctions for almost all phases; for the one dimensional quasi-periodic Schrodinger operators with small Gevrey potentials, the length of spectral gaps decays sub-exponentially with respect to its labelling; and the spectrum is an interval for discrete Schrodinger operators acting on Z(d) with small separable potentials.
引用
收藏
页码:6124 / 6155
页数:32
相关论文
共 50 条
  • [1] STRONG ALMOST REDUCIBILITY FOR ANALYTIC AND GEVREY QUASI-PERIODIC COCYCLES
    Chavaudret, Claire
    BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 2013, 141 (01): : 47 - 106
  • [2] RIGIDITY OF REDUCIBILITY OF GEVREY QUASI-PERIODIC COCYCLES ON U(n)
    Hou, Xuanji
    Popov, Georgi
    BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 2016, 144 (01): : 1 - 52
  • [3] Quantitative reducibility of Ck quasi-periodic cocycles
    Cai, Ao
    Lv, Huihui
    Wang, Zhiguo
    ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2024,
  • [4] Reducibility of Finitely Differentiable Quasi-Periodic Cocycles and Its Spectral Applications
    Cai, Ao
    Ge, Lingrui
    JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2022, 34 (03) : 2079 - 2104
  • [5] Reducibility of Finitely Differentiable Quasi-Periodic Cocycles and Its Spectral Applications
    Ao Cai
    Lingrui Ge
    Journal of Dynamics and Differential Equations, 2022, 34 : 2079 - 2104
  • [6] Embedding of Analytic Quasi-Periodic Cocycles into Analytic Quasi-Periodic Linear Systems and its Applications
    You, Jiangong
    Zhou, Qi
    COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2013, 323 (03) : 975 - 1005
  • [7] Embedding of Analytic Quasi-Periodic Cocycles into Analytic Quasi-Periodic Linear Systems and its Applications
    Jiangong You
    Qi Zhou
    Communications in Mathematical Physics, 2013, 323 : 975 - 1005
  • [8] LOCAL RIGIDITY OF REDUCIBILITY OF ANALYTIC QUASI-PERIODIC COCYCLES ON U(n)
    Hou, Xuanji
    You, Jiangong
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2009, 24 (02) : 441 - 454
  • [9] Rigidity of Reducibility of Finitely Differentiable Quasi-Periodic Cocycles on U(n)
    Huijuan Lai
    Xuanji Hou
    Jinhui Li
    Journal of Dynamics and Differential Equations, 2022, 34 : 2549 - 2577
  • [10] Rigidity of Reducibility of Finitely Differentiable Quasi-Periodic Cocycles on U(n)
    Lai, Huijuan
    Hou, Xuanji
    Li, Jinhui
    JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2022, 34 (03) : 2549 - 2577