Functional Analysis and Its Applications

, Volume 19, Issue 1, pp 34–39 | Cite as

Structure of the spectrum of the Schrödinger operator with almost-periodic potential in the vicinity of its left edge

  • Ya. G. Sinai


Functional Analysis Left Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    E. I. Dinaburg and Ya. G. Sinai, "On the one-dimensional Schrödinger equation with a quasiperiodic potential," Funkts. Anal. Prilozhen.,9, No. 4, 8–21 (1975).Google Scholar
  2. 2.
    E. D. Belokolos, "The quantum particle in a one-dimensional deformed lattice. Estimate of the sizes of the lacunas in the spectrum," Teor. Mat. Fiz.,25, No. 3, 344–357 (1975).Google Scholar
  3. 3.
    H. Rüssmann, "On the one-dimensional Schrödinger equation with a quasiperiodic potential," Ann. New York Acad. Sci.,357, 90–107 (1980).Google Scholar
  4. 4.
    J. Bellisard, R. Lima, and D. Testard, "A metal-insulator transition for almost Mathieu model," Commun. Math. Phys.,88, No. 2, 207–235 (1983).Google Scholar
  5. 5.
    S. Aubry, "The twist map, the extended Frenkel-Kotorova model and the Devil's staircase," Physica D7, 240–258 (1983).Google Scholar
  6. 6.
    J. Moser, "Lectures on Hamiltonian systems," Mem. Am. Math. Soc., No. 81, 1–60 (1968); C. L. Siegel and J. Moser, Lectures on Celestial Mechanics, Secs. 32–36, Springer-Verlag, Berlin-Heidelberg-New York (1971).Google Scholar
  7. 7.
    V. F. Lazutkin and D. Ya. Terman, "Percival's variational principle and commensurate-incommensurate phase transitions in one-dimensional chains," Commun. Math. Phys.,94, No. 4, 511–522 (1984).Google Scholar
  8. 8.
    S. M. Kozlov, "Reducibility of quasiperiodic operators and averaging," Tr. Mosk. Mat.46, 99–123 (1983).Google Scholar
  9. 9.
    J. Moser, "A rapidly convergent iteration method and nonlinear differential equations. I, II," Ann. Scuola Norm. Sup. Pisa, Ser. III,20, 265–316 and20, 499–535 (1966).Google Scholar
  10. 10.
    J. N. Mather, "Existence of quasiperiodic orbits for twist homeomorphisms of the annulus," Topology,21, 457–467 (1982).Google Scholar
  11. 11.
    I. C. Percival, "Variational principle for invariant tori and cantori. Nonlinear dynamics and the beam-beam interaction," AIP Conf. Proc., No. 57, 302–310 (1979).Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • Ya. G. Sinai

There are no affiliations available

Personalised recommendations