## Singular continuous spectrum for a class of almost periodic Jacobi matrices

HTML articles powered by AMS MathViewer

- by Joseph Avron and Barry Simon PDF
- Bull. Amer. Math. Soc.
**6**(1982), 81-85

## References

- Serge Aubry and Gilles André,
*Analyticity breaking and Anderson localization in incommensurate lattices*, Group theoretical methods in physics (Proc. Eighth Internat. Colloq., Kiryat Anavim, 1979) Ann. Israel Phys. Soc., vol. 3, Hilger, Bristol, 1980, pp. 133–164. MR**626837** - 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. MR**522493**
3. J. Avron and B. Simon, Almost periodic Schrödinger operators. II. The density of states and the André-Aubry Theorem (in preparation).
- Ju. M. Berezans′kiĭ,
*Expansions in eigenfunctions of selfadjoint operators*, Translations of Mathematical Monographs, Vol. 17, American Mathematical Society, Providence, R.I., 1968. Translated from the Russian by R. Bolstein, J. M. Danskin, J. Rovnyak and L. Shulman. MR**0222718**, DOI 10.1090/mmono/017 - A. Ja. Gordon,
*The point spectrum of the one-dimensional Schrödinger operator*, Uspehi Mat. Nauk**31**(1976), no. 4(190), 257–258 (Russian). MR**0458247**
6. R. Johnson, The recurrent Hill’s equation, U.S.C. preprint.
- V. I. Oseledec,
*A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems*, Trudy Moskov. Mat. Obšč.**19**(1968), 179–210 (Russian). MR**0240280**
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.
- D. B. Pearson,
*Singular continuous measures in scattering theory*, Comm. Math. Phys.**60**(1978), no. 1, 13–36. MR**484145**, DOI 10.1007/BF01609472 - Michael Reed and Barry Simon,
*Methods of modern mathematical physics. I*, 2nd ed., Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1980. Functional analysis. MR**751959** - 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. MR**556846**
12. M. Shubin, Density of states for self-adjoint elliptic operators with almost periodic coefficients, Trudy Sem. Petrovkii 3 (1978), 243.
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.

## Additional Information

- Journal: Bull. Amer. Math. Soc.
**6**(1982), 81-85 - MSC (1980): Primary 47A10, 47A25; Secondary 81Cxx
- DOI: https://doi.org/10.1090/S0273-0979-1982-14971-0
- MathSciNet review: 634437