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Analytic dependence of Lyapunov exponents on transition probabilities

  • Chapter 1: Linear Random Dynamical Systems
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Lyapunov Exponents

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1486))

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References

  1. P. Bougerol, Comparaison des exposants de Lyapunov des processus Markoviens multiplicatifs, Ann. Inst. Henri Poincaré 24 (1988), 439–489.

    MathSciNet  MATH  Google Scholar 

  2. P. Bougerol, Théorèmes limite pour les systèmes linéaires à coefficients Markoviens, Prob. Th. Rel. Fields 78 (1988), 193–221.

    Article  MathSciNet  MATH  Google Scholar 

  3. P. Bougerol and J. Lacroix, Products of Random Matrices with Applications to Schrödinger operators, Birkhauser, Basel 1985.

    Book  MATH  Google Scholar 

  4. H. Furstenberg, Non-commuting random products, Trans. Amer. Math. Soc. 108 (1963), 377–428.

    Article  MathSciNet  MATH  Google Scholar 

  5. H. Furstenberg and Y. Kifer, Random matrix products and measures on projective spaces, Israel J. Math. 10 (1983), 12–32.

    Article  MathSciNet  MATH  Google Scholar 

  6. I.Ya Goldsheid and G.A. Margulis, Lyapunov indices of a product of random matrices, Russian Math. Surveys 44:5 (1989), 11–71.

    Article  MathSciNet  MATH  Google Scholar 

  7. Y. Guivarch, Exposant caractéristiques des produits de matrices aléatoires en dépendence Markovienne, In “Probability measures on groups 7”, ed. H. Heyer, Lecture Notes in Mathematics 1064, Springer-Verlag 1984, 161–181.

    Google Scholar 

  8. Y. Guivarch and A. Raugi, Frontière de Furstenberg, propriétés de contraction et théorèmes de convergence, Zeit. für Wahr. und verw. Gebeite 69 (1985), 187–242.

    Article  MathSciNet  MATH  Google Scholar 

  9. Y. Guivarch and A. Raugi, Products of random matrices: convergence theorems, In “Random Matrices and their Applications,” J. Cohen, H. Kesten, and C. Newman editors, Contemporary Math. vol. 50, Amer. Math. Soc., Providence 1985.

    Google Scholar 

  10. T. Kato, Perturbation Theory for Linear Operators, Second Edition, Springer-Verlag 1976.

    Google Scholar 

  11. Y. Kifer, Ergodic Theory of Random Transformations, Birkhauser, Basel 1986.

    Book  MATH  Google Scholar 

  12. F. Ledrappier, Positivity of the exponent for stationary sequences of matrices, In “Lyapunov Exponents Proceedings,” L. Arnold and V. Whistutz editors, Lecture Notes in Mathematics 1186, Springer-Verlag 1986, 56–73.

    Google Scholar 

  13. E. Le Page, Théorèmes limites pour les produits de matrices aléatoires, In “Probability Measures on Groups,” ed. H. Heyer, Lecture Notes in Math. 928, Springer-Verlag 1982, 258–303.

    Google Scholar 

  14. E. Le Page, Régularité du plus grand exposant caractéristique des produits de matrices aléatoires indépendantes et applications, Ann. Inst. Henri Poincaré 25 (1989), 109–142.

    MATH  Google Scholar 

  15. Y. Peres, Domains of analytic continuation for the top Lyapunov exponent, Preprint 1990.

    Google Scholar 

  16. D. Ruelle, Analyticity properties of the characteristic exponents of random matrix products, Adv. Math. 32 (1979), 68–80.

    Article  MathSciNet  MATH  Google Scholar 

  17. E. Seneta, Non-negative matrices and Markov chains, Second Edition, Springer-Verlag 1981.

    Google Scholar 

  18. B. Simon and M. Taylor, Harmonic analysis on SL(2,R) and smoothness of the density of states in the one-dimensional Anderson model, Commun. Math. Phys. 101 (1985), 1–19.

    Article  MathSciNet  MATH  Google Scholar 

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Author notes

  1. Yuval Peres

    Present address: Mathematics Department, Stanford University, 94305, Stanford, CA

Authors and Affiliations

  1. The Hebrew University, Jerusalem

    Yuval Peres

Authors
  1. Yuval Peres
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Ludwig Arnold Hans Crauel Jean-Pierre Eckmann

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© 1991 Springer-Verlag

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Peres, Y. (1991). Analytic dependence of Lyapunov exponents on transition probabilities. In: Arnold, L., Crauel, H., Eckmann, JP. (eds) Lyapunov Exponents. Lecture Notes in Mathematics, vol 1486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086658

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  • DOI: https://doi.org/10.1007/BFb0086658

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54662-7

  • Online ISBN: 978-3-540-46431-0

  • eBook Packages: Springer Book Archive

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