![]() ![]() Yessen, W.: Spectral analysis of tridiagonal Fibonacci Hamiltonians. Sűto, A.: Schrödinger difference equation with deterministic ergodic potentials. Sűto, A.: Singular continuous spectrum on a set of zero Lebesgue measure for the Fibonacci Hamiltonian. Sűto, A.: The spectrum of a quasiperiodic Schrödinger operator. American Mathematical Society, Providence (2004) Simon, B.: Orthogonal Polynomaials on the Unit Circle. Ong, D.C.: Limit-periodic Verblunsky coefficients for orthogonal polynomials on the unit circle. Proceedings of the 9th AIMS Conference Special Issue, pp. Discrete and Continuous Dynamical Systems. In contrast, we also show that all skew Sturmian subshifts belong to the same flow equivalence class, since they are all eventually periodic. Ong, D.C.: Orthogonal polynomials on the unit circle with quasiperiodic Verblunsky coefficients have generic purely singular continuous spectrum. We show that all skew Sturmian subshifts have a conjugacy class of size two, regardless of their least period. Kaminaga, M.: Absence of point spectrum for a class of discrete Schrödinger operators with quasiperiodic potential. Gordon, A.: The point spectrum of the one-dimensional Schrödinger operator. Gesztesy, F., Zinchenko, M.: Weyl–Titchmarsh theory for CMV operators associated with orthogonal polynomials on the unit circle. ![]() Theory 173, 56–88 (2013)ĭamanik, David, Munger, Paul, Yessen, William: Orthogonal polynomials on the unit circle with Fibonacci Verblunsky coefficients, II. 305, 221–277 (2011)ĭamanik, D., Munger, P., Yessen, W.: Orthogonal polynomials on the unit circle with Fibonacci Verblunsky coefficients, I. ![]() Theory 144, 133–138 (2007)ĭamanik, D., Gorodetski, A.: Spectral and quantum dynamical properties of the weakly coupled Fibonacci Hamiltonian. Henri Poincaré 2, 101–108 (2001)ĭamanik, D., Lenz, D.: Uniform Szegő cocycles over strictly ergodic subshifts. 212, 191–204 (2000)ĭamanik, D.: Uniform singular continuous spectrum for the period doubling Hamiltonian. American Mathematical Society, Providence (2007)ĭamanik, D., Killip, R., Lenz, D.: Uniform spectral properties of one-dimensional quasicrystals, III. Proceedings of Symposia in Pure Mathematics, vol. (eds.) Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon’s 60th Birthday. They are parametrised by irrationals in the unit interval and built from a local homeomorphism associated to the subshift. In: Gesztesy, F., Deift, P., Galvez, C., Perry, P., Schlag, W. Sturmian subshifts and their C-algebras Kevin Aguyar Brix This paper investigates the structure of C-algebras built from one-sided Sturmian subshifts. American Mathematical Society, Providence (2000)ĭamanik, D.: Strictly ergodic subshifts and associated operators. (eds.) Directions in Mathematical Quasicrystals. arXiv:1210.5753 (2012)ĭamanik, D.: Gordon-type arguments in the spectral theory of one-dimensional quasicrystals. thesis, Rice University (2011)ĭamanik, D., Embree, M., Gorodetski, A.: Spectral properties of Schrödinger operators arising in the study of quasicrystals. Springer, Berlin (2008)ĭahl, J.: The spectrum of the off-diagonal Fibonacci operator. LXIII, 0464–0507 (2010)Ĭycon, H., Froese, R., Kirsch, W., Simon, B.: Schrödinger Operators with Applications to Quantum Mechanics and Global Geometry. 362, 29–56 (2003)Ĭantero, M.-J., Grünbaum, F.A., Moral, L., Velázquez, L.: Matrix-valued Szegö polynomials and quantum random walks. 125, 527–543 (1989)Ĭantero, M.-J., Moral, L., Velázquez, L.: Five-diagonal matrices and zeros of orthogonal polynomials on the unit circle. 135, 379–399 (1991)īellissard, J., Iochum, B., Scoppola, E., Testard, D.: Spectral properties of one-dimensional quasicrystals. Springer, Berlin (1990)īellisard, J., Bovier, A., Ghez, J.-M.: Spectral properties of a tight-binding Hamiltonian with period doubling potential. In: Waldshmidt, P., Luck, M., Moussa, J.M. arXiv:1304.0519 (2013)īellisard, J.: Spectral properties of Schrödinger’s operator with a Thue-Morse potential. Finally, we derive Laplace operators from the spectral triples andĬompare our construction with that of Pearson and Bellissard.Avila, A., Damanik, D., Zhang, Z.: Singular density of states measure for subshift and quasi-periodic Schrödinger operators. Moreover, we study the zeta-function of the spectral triple and relate itsĪbscissa of convergence to the complexity exponent of the subshift or the For repetitive tilings we show that if their patches haveĮqui-distributed frequencies then the two metrics are Lipschitz equivalent. For Sturmian subshifts this is equivalent to linear Prove that d_s and d are Lipschitz equivalent if and only if the subshift is When X is a subshift space, or a discrete tiling space, and d satisfiesĬertain bounds we advocate that the property of d_s and d to be LipschitzĮquivalent is a characterization of high order. We study its relation with the original metricĭ. (Submitted on ( v1), last revised (this version, v2)) Abstract: We construct spectral triples for compact metric spaces (X, d). ![]()
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