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Positivity of the exponent for stationary sequences of matrices

Part I: Products Of Random Matrices And Random Maps

Part of the Lecture Notes in Mathematics book series (LNM,volume 1186)

Keywords

  • Invariant Measure
  • Stationary Sequence
  • Jacobi Matrice
  • Positive Lebesgue Measure
  • Herglotz Function

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References

  1. H. FURSTENBERG: Non-commuting random products. Trans. Amer. Math. Soc. 108 (1963) p. 377–428.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Y. GUIVARC'H: Marches aléatoires à pas markovien. C.R.A.S. Paris 289 (1979) p. 211–213.

    MathSciNet  MATH  Google Scholar 

  3. M. de GUZMAN: Differentiation of integrals in Rn. Springer Lect. Notes in Maths. 481 (1975).

    Google Scholar 

  4. S. KOTANI: Lyapunov indices determine absolutely continuous spectra of stationary random one-dimensional Schrödinger operators. Proc. Kyoto Stoch. Conference (1982).

    Google Scholar 

  5. S. KULLBACK: Information theory and Statistics. Wiley-New-York (1959).

    MATH  Google Scholar 

  6. F. LEDRAPPIER: Quelques propriétés des exposants caractéristiques Ecole d'Eté de Probabilités XII Saint-Flour 1982 Springer Lect. Notes in Maths. 1097 (1984).

    Google Scholar 

  7. F. LEDRAPPIER, G. ROYER: Croissance exponentielle de certains produits aléatoires de matrices. C.R.A.S. Paris 290 (1980) p. 49–62.

    MathSciNet  MATH  Google Scholar 

  8. F. LEDRAPPIER, L.S. YOUNG: The metric entropy of diffeomorphisms I, II. Preprints M.S.R.I. 1984.

    Google Scholar 

  9. V. A. ROHLIN: On the fundamental ideas of measure theory. Amer. Math. Trans. (1) 10 (1962) p. 1–52.

    Google Scholar 

  10. G. ROYER: Croissance exponentielle de produits markoviens de matrices aléatoires. Ann. I.H.P. 16 (1980) p. 49–62.

    MathSciNet  MATH  Google Scholar 

  11. B. SIMON: Kotani theory for One-dimensional Stochastic Jacobi Matrices. Commun. Math. Phys. 89 (1983) p. 227–234.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. A. D. VIRTSER: On products of random matrices and operators. Th. Prob. Appl. 24 (1979) p. 367–377.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1986 Springer-Verlag

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Ledrappier, F. (1986). Positivity of the exponent for stationary sequences of matrices. In: Arnold, L., Wihstutz, V. (eds) Lyapunov Exponents. Lecture Notes in Mathematics, vol 1186. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076833

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  • DOI: https://doi.org/10.1007/BFb0076833

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16458-6

  • Online ISBN: 978-3-540-39795-3

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