On the multiplicative ergodic theorem for uniquely ergodic systems

Alex Furman

Annales de l'I.H.P. Probabilités et statistiques (1997)

  • Volume: 33, Issue: 6, page 797-815
  • ISSN: 0246-0203

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Furman, Alex. "On the multiplicative ergodic theorem for uniquely ergodic systems." Annales de l'I.H.P. Probabilités et statistiques 33.6 (1997): 797-815. <http://eudml.org/doc/77590>.

@article{Furman1997,
author = {Furman, Alex},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {uniform convergence; multiplicative ergodic theorem; Lyapunov exponents},
language = {eng},
number = {6},
pages = {797-815},
publisher = {Gauthier-Villars},
title = {On the multiplicative ergodic theorem for uniquely ergodic systems},
url = {http://eudml.org/doc/77590},
volume = {33},
year = {1997},
}

TY - JOUR
AU - Furman, Alex
TI - On the multiplicative ergodic theorem for uniquely ergodic systems
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1997
PB - Gauthier-Villars
VL - 33
IS - 6
SP - 797
EP - 815
LA - eng
KW - uniform convergence; multiplicative ergodic theorem; Lyapunov exponents
UR - http://eudml.org/doc/77590
ER -

References

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  1. [1] J.E. Cohen, H. Kesten and M. Newman (editors), Oseledec's multiplicative ergodic theorem: a proof, Contemporary Mathematics, Vol. 50, 1986, pp. 23-30. Zbl0607.60026
  2. [2] H. Furstenberg and H. Kesten, Products of random matrices, Ann. Math. Stat., Vol. 31, 1960, pp. 457-489. Zbl0137.35501MR121828
  3. [3] E. Glasner and B. Weiss, On the construction of minimal skew-products, Israel J. Math., Vol. 34, 1979, pp. 321-336. Zbl0434.54032MR570889
  4. [4] M.R. Herman, Construction d'un difféomorphisme minimal d'entropie topologique non nulle, Ergod. Th. and Dyn. Sys., Vol. 1, No. 1, 1981, pp. 65-76. Zbl0469.58008MR627787
  5. [5] Y. Katznelson and B. Weiss, A simple proof of some ergodic theorems, Israel J. Math., Vol. 42, No. 4, 1982, pp. 291-296. Zbl0546.28013MR682312
  6. [6] J.F.C. Kingman, The ergodic theory of subadditive stochastic processes, J. Royal Stat. Soc., Vol. B30, 1968, pp. 499-510. Zbl0182.22802MR254907
  7. [7] O. Knill, The upper Lyapunov exponent of SL2(R) cocycles: discontinuity and the problem of positivity, in Lecture Notes in Math., Vol. 1186, Lyapunov exponents, Berlin-Heidelberg-New York, pp. 86-97. Zbl0746.58050MR1178949
  8. [8] O. Knill, Positive Lyapunov exponents for a dense set of bounded measurable SL2 (R)- cocycles, Ergod. Th. and Dyn. Syst., Vol. 12, No.2, 1992, pp. 319-331. Zbl0759.58025MR1176626
  9. [9] M.G. Nerurkar, Typical SL2 (R) valued cocycles arising from strongly accessible linear differential systems have non-zero Lyapunov exponents, preprint. 
  10. [10] V.I. Oseledec, A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems. Trans. Moscow Math. Soc., Vol. 19, 1968, pp. 197-231. Zbl0236.93034MR240280
  11. [11] P. Walters, Unique ergodicity and matrix products, in Lecture Notes in Math., Vol 1186, Lyapunov exponents, Berlin-Heidelberg-New York, pp. 37-56. Zbl0604.60011

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