The monodromization and Harper equation

V. Buslaev; A. Fedotov

Séminaire Équations aux dérivées partielles (Polytechnique) (1993-1994)

  • page 1-21

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Buslaev, V., and Fedotov, A.. "The monodromization and Harper equation." Séminaire Équations aux dérivées partielles (Polytechnique) (1993-1994): 1-21. <http://eudml.org/doc/112086>.

@article{Buslaev1993-1994,
author = {Buslaev, V., Fedotov, A.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {Harper equation; monodromization},
language = {eng},
pages = {1-21},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {The monodromization and Harper equation},
url = {http://eudml.org/doc/112086},
year = {1993-1994},
}

TY - JOUR
AU - Buslaev, V.
AU - Fedotov, A.
TI - The monodromization and Harper equation
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1993-1994
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 21
LA - eng
KW - Harper equation; monodromization
UR - http://eudml.org/doc/112086
ER -

References

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  1. [B-F1] V. Buslaev, A. Fedotov, Complex WKB method for Harper equation, Reports of Mittag-Leffler Institute11 (1993). 
  2. [B-F2] V. Buslaev, A. Fedotov, The functional structure of a monodormy matrix for Harper equation, Operator Theory: Advances and Applications (I.Gohberg, eds.), 1994. 
  3. [B-F3] V. Buslaev, A. Fedotov, On a class of matrices related to Harper equation, Reports of Mittag-Leffler Institute19 (1993). 
  4. [B-F4] V. Buslaev, A. Fedotov, Complex WKB method for Harper equation. I., Algebra and Analysis (in russian) No 4 (1994). Zbl0821.34062MR1301830
  5. [C-F-K-S] H.L. Cycon, R.G. Froese, W. Kirsch, B. Simon, Schrdinger operators, Springer-Verlag, 1987. 
  6. [Ho] D. Hofstadter, Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields, Phys. Rev.B14 (1976), 2239-2249. 
  7. [H-S] B. Helffer, J. Sjöstrand, Analyse semi-classique pour l'equation de Harper (avec application a'l etude de l'equation de Schrödinger avec champ magnétique), Mémoires de la SMF34 (1988). Zbl0714.34130
  8. [H-K-S] B. Helffer, P. Kerdelhué, J. Sjöstrand, Le papillon de Hofstadter revisité, Mémoires de la SMF43 (1990). Zbl0732.44004MR1090467
  9. [K] A. Ya. Khinchin, Continued fractions, Phoenix Science Series, 1964. MR161833
  10. [L] Y. LastZero mesure spectrum for the almost Mathieu operator, Preprint (March 1994). Zbl0814.11040MR1289331
  11. [O] V.I. Oseledets, A multiplicative ergodic theorem, Trans. Mosc. Math. Soc.19 (1969), 197-231. Zbl0236.93034
  12. [Wi] M. Wilkinson, Critical properties of electron eigenstates in incommensurate systems., Proc. Royal Society of London. A391 (1984), 305-350. MR739684
  13. [Y] J.C. Yoccoz, Ph.D. thesis. 

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