References
- Avila , A. and Jitomirskaya , S. “ The ten martini problem ” . eprint: arXiv:math.DS/0503363
- Beardon , A.F. , Bullett , S.R. and Rippon , J. 1995 . Periodic orbits of difference equations . Proceedings of the Royal Society of Edinburgh, Series A (Mathematics) , 125A : 657 – 674 .
- Bellissard , J. 1992 . “ Gap labelling theorems for Schrödinger operators ” . In From Number Theory to Physics , Edited by: Waldschmidt , M. , Moussa , P. , Luck , J.-M. and Itzykson , C. 538 – 630 . New York : Springer-Verlag .
- Bellissard, J., Le papillon de Hofstadter, (d'apres B. Helffer et J. Sjöstrand), Seminar Bourbaki, Vol. 1991/92, Astérisque No. 206 (1992), Exp. No. 745, pp. –39
- Bougerol , P. and Lacroix , J. 1985 . Products of Random Matrices with Applications to Schrödinger Operators , 187ff Boston : Birkhäuser .
- Brown , M. 1983 . American Mathematical Monthly , 90 : 569 [Solution, ibid 92 (1985), 218–219.]
- Collet , P. and Levy , Y. 1984 . Ergodic properties of the Lozi mappings . Communications in Mathematical Physics , 93 : 461 – 481 .
- Delyon , F. and Petritis , D. 1986 . Absences of localization in a class of Schrödinger operators with quasiperiodic potential . Communications in Mathematical Physics , 103 : 441 – 444 .
- Froeschlè , C. 1968 . Étude numérique de transformations ponctuelles planes conservant les aires . Comptes Rendus De L Academic Des Science Series II Paris , 266 : 846 – 848 .
- Herman , M. 1979 . Sur la conjugasion differentiable des difféomorphismes du cercle . Publication Mathematiques IHES , 49 : 5 – 234 .
- Herman , M. 1986 . Sur les Courbes Invariantes par les Difféomorphismes de l'Anneau. . Social Mathematics , 2, Astérisque 144, de France, Paris
- Hofstadter , D. 1976 . Energy levels and wave functions of Bloch electrons in a rational or irrational magnetic field . Physical Review B , 14 : 2239 – 2249 .
- Jitomirskaya , S. 1999 . Metal-insulator transition for the almost Mathieu operator . Annals of Mathematics , 150 : 1159 – 1175 .
- Kotani , S. 1990 . Jacobi matrices with random potential taking finitely many values . Reviews of Mathematical Physics , 1 : 129 – 133 .
- Lagarias , J.C. and Rains , E. Dynamics of a family of piecewise-linear area-preserving plane maps II. Invariant circles . Journal of Difference Equations and Applications , in press
- Lagarias , J.C. and Rains , E. “ Dynamics of a family of piecewise-linear area-preserving plane maps III. Cantor set spectra ” . In Journal of Difference Equations and Applications in press
- Lozi , R. 1979 . “ Strange attractors: a class of mappings of ℝ2 which leaves some Cantor sets invariant ” . In Intrinsic Stochasticity in Plasmas (Internat. Workshop, Inst. Etudes Sci. Cargèse, Cargèse 1979 , 373 – 381 . Palaiseau : Ecole Polytech. .
- Misiurewicz , M. 1980 . Strange attractors for the Lozi mappings . Nonlinear Dynamics, New York 1979 , : 348 – 358 . Ann. New York Acad. Sci. 357, New York Acad. Sci.
- Nitecki , Z. 1971 . Differentiable Dynamics: An Introduction to the Orbit Structure of Diffeomorphisms , Cambridge, MA : MIT Press .
- Pastur , L. and Figotin , A. 1992 . Spectra of Random and Almost-Periodic Operators , Berlin : Springer-Verlag . Grund. Math. Wiss, 297
- Puig , J. 2004 . Cantor spectrum for the almost Mathieu operator . Communications in Mathematical Physics , 244 : 297 – 309 .
- Sjóstrand , J. 1991 . “ Microlocal analysis for the periodic magnetic Schrödinger equation and related questions ” . In Microlocal Analysis and Applications (Motecatini Terme, 1989) , 237 – 332 . Berlin : Springer-Verlag . Lecture Notes in Math. 1495
- Spencer , T. 1986 . Random and quasiperiodic Schrödinger operators . Proceedings of the International Congress of Mathematicians , II : 1312 – 1318 . Berkeley
- Sutherland , B. and Kohmoto , M. 1987 . Resistance of a one-dimensional quasicrystal: Power-law growth . Physical Review B , 36 : 5877 – 5886 .
- Sütö , A. 1995 . “ Schrödinger difference equation with deterministic ergodic potentials ” . In Beyond Quasicrystals (Les Houches 1994) , 481 – 549 . New York : Springer-Verlag .
- Wan , Yi and Soukoulis , C.M. 1990 . One-dimensional nonlinear Schrödinger equation: a nonlinear dynamics approach . Physical Review A , 41 : 800 – 809 .