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A dynamical proof of the multiplicative ergodic theorem


Author: Peter Walters
Journal: Trans. Amer. Math. Soc. 335 (1993), 245-257
MSC: Primary 28D05; Secondary 58F11
DOI: https://doi.org/10.1090/S0002-9947-1993-1073779-7
MathSciNet review: 1073779
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Abstract: We shall give a proof of the following result of Oseledec, in which $ GL(d)$ denotes the space of invertible $ d \times d$ real matrices, $ \vert\vert \bullet \vert\vert$ denotes any norm on the space of $ d \times d$ matrices, and $ {\log ^+ }(t) = \max (0,\log (t))$ for $ t \in [0,\infty )$.


References [Enhancements On Off] (What's this?)

  • [1] N. Bourbaki, Intégration, Vol. VI, Chapitre 6, Hermann, Paris, 1959.
  • [2] C. Castaing and M. Valadier, Convex analysis and measurable multifunctions, Lecture Notes in Math., Vol. 580, Springer-Verlag, Berlin and New York, 1975. MR 0467310 (57:7169)
  • [3] J. E. Cohen, H. Kesten, and C. M. Newman (eds.), Random matrices and their applications, Comtemp. Math., Vol. 50, Amer. Math. Soc., Providence, R. I., 1984. MR 841077 (87a:60006)
  • [4] H. Crauel, Lyapunov exponents and invariant measures of stochastic systems on manifolds, Lecture Notes in Math., Vol. 1186, Springer-Verlag, Berlin and New York, 1985, pp. 271-291. MR 850084 (88b:58116)
  • [5] M. W. Hirsch, Differential topology, Graduate Texts in Math., Vol. 33, Springer-Verlag, Berlin and New York, 1976. MR 0448362 (56:6669)
  • [6] F. Ledrappier, Quelques proprietes des exposants caracteristiques, Lecture Notes in Math., Vol. 1098, Springer-Verlag, Berlin and New York, 1984, pp. 306-396. MR 876081 (88b:58081)
  • [7] V. I. Oseledec, A multiplicative ergodic theorem and Lyapunov characteristic numbers for dynamical systems, Trans. Moscow Math. Soc. 19 (1968), 197-231. MR 0240280 (39:1629)
  • [8] Ya. B. Pesin, Characteristic Lyapunov exponents and smooth ergodic theory, Russian Math. Surveys 32 (1977), 55-114. MR 0466791 (57:6667)
  • [9] M. S. Raghunathan, A proof of Oseledec's multiplicative ergodic theorem, Israel J. Math. 32 (1979), 356-362. MR 571089 (81f:60016)
  • [10] D. Ruelle, Ergodic theory of differentiable dynamical systems, Inst. Hautes Études Sci. Publ. Math. 50 (1979), 27-58. MR 556581 (81f:58031)
  • [11] A. Ionescu Tulcea and C. Ionescu Tulcea, Topics in the theory of lifting, Ergeb. Math., Grenzgeb., Vol. 48, Springer-Verlag, Berlin and New York, 1969. MR 0276438 (43:2185)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1993-1073779-7
Keywords: Ergodic theorem, measure-preserving, ergodic
Article copyright: © Copyright 1993 American Mathematical Society

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