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Singular continuous spectrum for a class of almost periodic Jacobi matrices. (English) Zbl 0491.47014


MSC:

47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47A10 Spectrum, resolvent
47A25 Spectral sets of linear operators
81Q99 General mathematical topics and methods in quantum theory
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[2] Serge Aubry, The new concept of transitions by breaking of analyticity in a crystallographic model, Solitons and condensed matter physics (Proc. Sympos. Nonlinear (Soliton) Structure and Dynamics in Condensed Matter, Oxford, 1978) Springer Ser. Solid-State Sci., vol. 8, Springer, Berlin-New York, 1978, pp. 264 – 277.
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[8] L. Pasteur and M. Benderskii, On the spectrum of the one-dimensional Schrödinger equation with a random potential, Mat. U.S.S.R. Sb. 11 (1970), 245.
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[11] David Ruelle, Sensitive dependence on initial condition and turbulent behavior of dynamical systems, Bifurcation theory and applications in scientific disciplines (Papers, Conf., New York, 1977) Ann. New York Acad. Sci., vol. 316, New York Acad. Sci., New York, 1979, pp. 408 – 416.
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[13] D. Thouless, A relation between the density of states and range of localization for one dimensional random system, J.Phys. C 5 (1972), 77-81.
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