Existence of non-uniform cocycles on uniquely ergodic systems
Annales de l'I.H.P. Probabilités et statistiques (2004)
- Volume: 40, Issue: 2, page 197-206
- ISSN: 0246-0203
Access Full Article
topHow to cite
topReferences
top- [1] G. Andre, S. Aubry, Analyticity breaking and Anderson localization in incommensurate lattices, Ann. Israel Phys. Soc.3 (1980) 133-140. Zbl0943.82510MR626837
- [2] J. Avron, B. Simon, Singular continuous spectrum for a class of almost periodic Jacobi matrices, Bull. Amer. Math. Soc.6 (1982) 81-85. Zbl0491.47014MR634437
- [3] R. Carmona, J. Lacroix, Spectral Theory of Random Schrödinger Operators, Birkhäuser, Boston, 1990. Zbl0717.60074MR1102675
- [4] H.L. Cycon, R.G. Froese, W. Kirsch, B. Simon, Schrödinger Operators with Application to Quantum Mechanics and Global Geometry, Springer, Berlin, 1987. Zbl0619.47005MR883643
- [5] F. Durand, Linearly recurrent subshifts have a finite number of non-periodic subshift factors, Ergodic Theory Dynamical Systems20 (2000) 1061-1078. Zbl0965.37013MR1779393
- [6] A. Furman, On the multiplicative ergodic theorem for uniquely ergodic ergodic systems, Ann. Inst. Henri Poincaré Probab. Statist.33 (1997) 797-815. Zbl0892.60011MR1484541
- [7] H. Furstenberg, B. Weiss, Private communication.
- [8] M.-R. Herman, Construction d'un difféomorphisme minimal d'entropie non nulle, Ergodic Theory Dynamical Systems1 (1981) 65-76. Zbl0469.58008MR627787
- [9] M.-R. Herman, Une méthode pour minorer les exposants de Lyapunov et quelques exemples montrant the caractère local d'un théorème d'Arnold et de Moser sur le tore de dimension 2, Comment. Math. Helv58 (1983) 453-502. Zbl0554.58034MR727713
- [10] S. Jitomirskaya, Almost everything about the almost-Mathieu operator, II, in: XIth International Congress of Mathematical Physics (Paris, 1994), Internat. Press, Cambridge, MA, 1995, pp. 373-382. Zbl1052.82539MR1370694
- [11] S. Jitomirskaya, Metal-insulator transition for the almost-Mathieu operator, Ann. of Math. (2)150 (1999) 1159-1175. Zbl0946.47018MR1740982
- [12] O. Knill, The upper Lyapunov exponent of SL(2,R) cocycles: discontinuity and the problem of positivity, in: Lyapunov Exponents (Oberwolfach, 1990), Lecture Notes in Math., vol. 1486, Springer, Berlin, 1991, pp. 86-97. Zbl0746.58050MR1178949
- [13] Y. Last, Almost everything about the almost-Mathieu operator, I, in: XIth International Congress of Mathematical Physics (Paris, 1994), Internat. Press, Cambridge, MA, 1995, pp. 373-382. Zbl1052.82539MR1370693
- [14] Y. Last, B. Simon, Eigenfunctions, transfer matrices, and absolutely continuous spectrum for one-dimensional Schrödinger operators, Invent. Math.135 (1999) 329-367. Zbl0931.34066MR1666767
- [15] D. Lenz, Random operators and crossed products, Mathematical Physics Analysis and Geometry2 (1999) 197-220. Zbl0965.47024MR1733886
- [16] D. Lenz, Singular spectrum of Lebesgue measure zero for one-dimensional quasicrystals, Comm. Math. Phys.227 (2002) 129-130. Zbl1065.47035MR1903841
- [17] D. Lenz, Uniform ergodic theorems on subshifts over a finite alphabet, Ergodic Theory Dynamical Systems22 (2002) 245-255. Zbl1004.37005MR1889573
- [18] D. Lenz, Hierarchical structures in Sturmian dynamical systems, Theoret. Comput. Sci.303 (2003) 463-490. Zbl1027.37006MR1990777
- [19] D. Ruelle, Ergodic theory of differentiable dynamical systems, Inst. Hautes Études Sci. Publ. Math.50 (1979) 27-58. Zbl0426.58014MR556581
- [20] W.A. Veech, Strict ergodicity in zero-dimensional dynamical systems and the Kronecker–Weyl theorem modulo 2, Trans. Amer. Math. Soc.140 (1969) 1-33. Zbl0201.05601
- [21] P. Walters, Unique ergodicity and random matrix products, in: Lyapunov Exponents (Bremen, 1984), Lecture Notes in Math., vol. 1186, Springer, Berlin, 1986, pp. 37-55. Zbl0604.60011MR850069