Existence of non-uniform cocycles on uniquely ergodic systems
Lenz, Daniel
Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004), p. 197-206 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPB_2004__40_2_197_0,
     author = {Lenz, Daniel},
     title = {Existence of non-uniform cocycles on uniquely ergodic systems},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {40},
     year = {2004},
     pages = {197-206},
     doi = {10.1016/j.anihpb.2003.04.002},
     mrnumber = {2044815},
     zbl = {1042.37002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2004__40_2_197_0}
}

Lenz, Daniel. Existence of non-uniform cocycles on uniquely ergodic systems. Annales de l'I.H.P. Probabilités et statistiques, Tome 40 (2004) pp. 197-206. doi : 10.1016/j.anihpb.2003.04.002. http://gdmltest.u-ga.fr/item/AIHPB_2004__40_2_197_0/

[1] G. Andre, S. Aubry, Analyticity breaking and Anderson localization in incommensurate lattices, Ann. Israel Phys. Soc. 3 (1980) 133-140. | MR 626837 | Zbl 0943.82510

[2] J. Avron, B. Simon, Singular continuous spectrum for a class of almost periodic Jacobi matrices, Bull. Amer. Math. Soc. 6 (1982) 81-85. | MR 634437 | Zbl 0491.47014

[3] R. Carmona, J. Lacroix, Spectral Theory of Random Schrödinger Operators, Birkhäuser, Boston, 1990. | MR 1102675 | Zbl 0717.60074

[4] H.L. Cycon, R.G. Froese, W. Kirsch, B. Simon, Schrödinger Operators with Application to Quantum Mechanics and Global Geometry, Springer, Berlin, 1987. | MR 883643 | Zbl 0619.47005

[5] F. Durand, Linearly recurrent subshifts have a finite number of non-periodic subshift factors, Ergodic Theory Dynamical Systems 20 (2000) 1061-1078. | MR 1779393 | Zbl 0965.37013

[6] A. Furman, On the multiplicative ergodic theorem for uniquely ergodic ergodic systems, Ann. Inst. Henri Poincaré Probab. Statist. 33 (1997) 797-815. | Numdam | MR 1484541 | Zbl 0892.60011

[7] H. Furstenberg, B. Weiss, Private communication.

[8] M.-R. Herman, Construction d'un difféomorphisme minimal d'entropie non nulle, Ergodic Theory Dynamical Systems 1 (1981) 65-76. | MR 627787 | Zbl 0469.58008

[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. Helv 58 (1983) 453-502. | MR 727713 | Zbl 0554.58034

[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. | MR 1370694 | Zbl 1052.82539

[11] S. Jitomirskaya, Metal-insulator transition for the almost-Mathieu operator, Ann. of Math. (2) 150 (1999) 1159-1175. | MR 1740982 | Zbl 0946.47018

[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. | MR 1178949 | Zbl 0746.58050

[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. | MR 1370693 | Zbl 1052.82539

[14] Y. Last, B. Simon, Eigenfunctions, transfer matrices, and absolutely continuous spectrum for one-dimensional Schrödinger operators, Invent. Math. 135 (1999) 329-367. | MR 1666767 | Zbl 0931.34066

[15] D. Lenz, Random operators and crossed products, Mathematical Physics Analysis and Geometry 2 (1999) 197-220. | MR 1733886 | Zbl 0965.47024

[16] D. Lenz, Singular spectrum of Lebesgue measure zero for one-dimensional quasicrystals, Comm. Math. Phys. 227 (2002) 129-130. | MR 1903841 | Zbl 1065.47035

[17] D. Lenz, Uniform ergodic theorems on subshifts over a finite alphabet, Ergodic Theory Dynamical Systems 22 (2002) 245-255. | MR 1889573 | Zbl 1004.37005

[18] D. Lenz, Hierarchical structures in Sturmian dynamical systems, Theoret. Comput. Sci. 303 (2003) 463-490. | MR 1990777 | Zbl 1027.37006

[19] D. Ruelle, Ergodic theory of differentiable dynamical systems, Inst. Hautes Études Sci. Publ. Math. 50 (1979) 27-58. | Numdam | MR 556581 | Zbl 0426.58014

[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. | Zbl 0201.05601

[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. | MR 850069 | Zbl 0604.60011