[1] Avila A. The absolutely continuous spectrum of the almost Mathieu operator. arXiv, 2008, 0810.2965 [2] Avila A, Jitomirskaya S. Almost localization and almost reducibility. J Eur Math Soc, 2010, 12:93-131 [3] Avila A, Jitomirskaya S. Hölder continuity of absolutely continuous spectral measures for one-frequency Schrödinger operators. Comm Math Phys, 2011, 301(2):563-581 [4] Avila A, Jitomirskaya S, Marx C A. Spectral theory of extended Harper's model and a question by Erdos and Szekeres. Invent Math, 2017, 210(1):283-339 [5] Bourgain J. Hölder regularity of integrated density of states for the almost Mathieu operator in a perturbative regime. Lett Math Phys, 2000, 51(2):83-118 [6] Cai A, Chavaudret C, You J G, Zhou Q. Sharp Hölder continuity of the Lyapunov exponent of finitely differentiable quasi-periodic cocycles. Math Z, 2019, 29(3/4):931-958 [7] Damanik D, Goldstein M, Lukic M. The spectrum of a Schrödinger operator with small quasi-periodic potential is homogeneous. J Spectral Theory, 2016, 6(2):415-427 [8] Delyon F, Souillard B. The rotation number for finite difference operators and its properties. Comm Math Phys, 1983, 89(3):415-426 [9] Fillman J, Lukic M. Spectral homogeneity of limit-periodic Schrödinger operators. J Spectr Theory, 2017, 7(2):387-406 [10] Damanik D, Goldstein M, Schlag W, Voda M. Homogeneity of the spectrum for quasi-perioidic Schrödinger operators. J Eur Math Soc, 2018, 20(12):3073-3111 [11] Goldstein M, Schlag W. Hölder continuity of the integrated density of states for quasi-periodic Schrödinger equations and averages of shifts of subharmonic functions. Ann Math, 2001, 154(1):155-203 [12] Goldstein M, Schlag W, Voda M. On localization and the spectrum of multi-frequency quasi-periodic operators. arXiv, 2016, 1610.00380 [13] Hadj Amor S. Hölder continuity of the rotation number for quasi-periodic co-cycles in SL(2, R). Comm Math Phys, 2009, 287(2):565-588 [14] Han R. Absence of point spectrum for the self-dual extended Harper's model. Int Math Res Not, 2018, (9):2801-2809 [15] Han R. Dry Ten Martini problem for the non-self-dual extended Harper's model. Trans Amer Math Soc, 2018, 370(1):197-217 [16] Han R, Jitomirskaya S. Full measure reducibility and localization for quasiperiodic Jacobi operators:a topological criterion. Adv Math, 2017, 319:224-250 [17] Han R, Yang F, Zhang S W. Spectral dimension for β-almost periodic singular Jacobi operators and the extended Harper's model. arXiv, 2018, 1804.04322 [18] Han R, Zhang S W. Optimal large deviation estimates and Hölder regularity of the Lyapunov exponents for quasi-periodic Schrödinger cocycles. arXiv, 2018, 1803.02035 [19] Jitomirskaya S, Koslover D A, Schulteis M S. Localization for a family of one-dimensional quasiperiodic operators of magnetic origin. Ann Henri Poincaré, 2005, 6(1):103-124 [20] Johnson R, Moser J. The rotation number for almost periodic potentials. Comm Math Phys, 1983, 90(2):317-318 [21] Leguil M, You J G, Zhao Z Y, Zhou Q. Asymptotics of spectral gaps of quasi-periodic Schrödinger operators. arXiv, 2017, 1712.04700 [22] Liu W C, Shi Y F. Upper bounds on the spectral gaps of quasi-periodic Schrödinger operators with Liouville frequencies. To appear in J Spectr Theory [23] Liu W C, Yuan X P. Hölder continuity of the spectral measures for one-dimensional Schrödinger operator in exponential regime. J Math Phys, 2015, 56(1):012701-21 [24] Shi Y F, Yuan X P. Exponential decay of the lengths of the spectral gaps for the extended Harper's model with a Liouvillean frequency. To appear in J Dynam Differential Equations [25] Tao K. Strong Birkhoff ergodic theorem for subharmonic functions with irrational shift and its application to analytic quasi-periodic cocycles. arXiv, 2018, 1805.00431 [26] Tao K, Voda M. Hölder continuity of the integrated density of states for quasi-periodic Jacobi operators. J Spectr Theory, 2017, 7(2):361-386 [27] Thouless D J. Bandwidths for a quasiperiodic tight-binding model. Phys Rev B, 1983, 28(8):4272-4276 [28] You J G, Zhang S W. Hölder continuity of the Lyapunov exponent for analytic quasiperiodic Schrödinger cocycle with weak Liouville frequency. Ergodic Theory Dynam Systems, 2014, 34(4):1395-1408 |