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Tr. Mosk. Mat. Obs., 1968, Volume 19, Pages 179–210 (Mi mmo214)  

This article is cited in 38 scientific papers (total in 38 papers)

A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems

V. I. Oseledets


Full text: PDF file (4710 kB)

English version:
Transactions of the Moscow Mathematical Society, 1968, 19, 197–231

Bibliographic databases:
UDC: 517.863
MSC: Primary 28.70; Secondary 34.00

Citation: V. I. Oseledets, “A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems”, Tr. Mosk. Mat. Obs., 19, MSU, M., 1968, 179–210; Trans. Moscow Math. Soc., 19 (1968), 197–231

Citation in format AMSBIB
\Bibitem{Ose68}
\by V.~I.~Oseledets
\paper A multiplicative ergodic theorem. Characteristic Ljapunov, exponents of dynamical systems
\serial Tr. Mosk. Mat. Obs.
\yr 1968
\vol 19
\pages 179--210
\publ MSU
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo214}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=240280}
\zmath{https://zbmath.org/?q=an:0236.93034}
\transl
\jour Trans. Moscow Math. Soc.
\yr 1968
\vol 19
\pages 197--231


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. M. Millionshchikov, “A stability criterion for the probability spectrum of linear systems of differential equations with recurrent coefficients and a criterion for almost reducibility of systems with almost periodic coefficients”, Math. USSR-Sb., 7:2 (1969), 171–193  mathnet  crossref  mathscinet
    2. Ya. B. Pesin, “Families of invariant manifolds corresponding to nonzero characteristic exponents”, Math. USSR-Izv., 10:6 (1976), 1261–1305  mathnet  crossref  mathscinet  zmath
    3. Ya. B. Pesin, “Geodesic flows on closed Riemannian manifolds without focal points”, Math. USSR-Izv., 11:6 (1977), 1195–1228  mathnet  crossref  mathscinet  zmath
    4. Ya. B. Pesin, “Characteristic Lyapunov exponents and smooth ergodic theory”, Russian Math. Surveys, 32:4 (1977), 55–114  mathnet  crossref  mathscinet  zmath
    5. Ya. B. Pesin, “A formula for the hausdorff measure of a twodimensional hyperbolic attractor”, Funct. Anal. Appl., 16:4 (1982), 313–315  mathnet  crossref  mathscinet  zmath  isi
    6. Nguyen Dinh Cong, “On the stochastic stability of the Lyapunov exponents of equations of arbitrary order”, Math. USSR-Sb., 60:1 (1988), 217–235  mathnet  crossref  mathscinet  zmath
    7. Yu. D. Latushkin, A. M. Stepin, “Weighted shift operator on a topological Markov chain”, Funct. Anal. Appl., 22:4 (1988), 330–331  mathnet  crossref  mathscinet  zmath  isi
    8. I. Ya. Gol'dsheid, G. A. Margulis, “Lyapunov indices of a product of random matrices”, Russian Math. Surveys, 44:5 (1989), 11–71  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. Yu. D. Latushkin, A. M. Stepin, “Weighted shift operator, spectral theory of linear extensions, and the Multiplicative Ergodic Theorem”, Math. USSR-Sb., 70:1 (1991), 143–163  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    10. Yu. D. Latushkin, A. M. Stepin, “Weighted translation operators and linear extensions of dynamical systems”, Russian Math. Surveys, 46:2 (1991), 95–165  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    11. N. I. Chernov, “New proof of Sinai's formula for the entropy of hyperbolic billiard systems. Application to Lorentz gases and Bunimovich stadiums”, Funct. Anal. Appl., 25:3 (1991), 204–219  mathnet  crossref  mathscinet  zmath  isi
    12. A. V. Letchikov, “Asymptotic properties with probability 1 for one-dimensional random walks in a random environment”, Math. USSR-Sb., 74:2 (1993), 455–473  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    13. E. A. Sataev, “Invariant measures for hyperbolic maps with singularities”, Russian Math. Surveys, 47:1 (1992), 191–251  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    14. A. V. Letchikov, “A criterion for linear drift, and the central limit theorem for one-dimensional random walks in a random environment”, Russian Acad. Sci. Sb. Math., 79:1 (1994), 73–92  mathnet  crossref  mathscinet  zmath  isi
    15. N. I. Chernov, “On Local Ergodicity in Hyperbolic Systems with Singularities”, Funct. Anal. Appl., 27:1 (1993), 51–54  mathnet  crossref  mathscinet  zmath  isi
    16. G. G. Malinetskii, G. Z. Tsertsvadze, “The investigation of the Lyapunov spectrum of the Kuramoto–Tsuzuki equation”, Comput. Math. Math. Phys., 33:7 (1993), 919–927  mathnet  mathscinet  zmath  isi
    17. A. V. Letchikov, “Conditional limit theorem for products of random matrices”, Sb. Math., 186:3 (1995), 371–389  mathnet  crossref  mathscinet  zmath  isi
    18. A. V. Letchikov, “Products of unimodular independent random matrices”, Russian Math. Surveys, 51:1 (1996), 49–96  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    19. V. Yu. Protasov, “On the regularity of de Rham curves”, Izv. Math., 68:3 (2004), 567–606  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    20. V. N. Krupchatnikov, I. V. Borovko, “Nekotorye osobennosti dinamiki polyarnogo vikhrya”, Sib. zhurn. vychisl. matem., 8:4 (2005), 325–335  mathnet  zmath
    21. V. Yu. Protasov, “Fractal curves and wavelets”, Izv. Math., 70:5 (2006), 975–1013  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    22. Y. Guivarc'h, “On contraction properties for products of Markov driven random matrices”, Zhurn. matem. fiz., anal., geom., 4:4 (2008), 457–489  mathnet  mathscinet  zmath  elib
    23. A. Yu. Kolesov, N. Kh. Rozov, “On the definition of ‘chaos’”, Russian Math. Surveys, 64:4 (2009), 701–744  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    24. A. Yu. Loskutov, “Fascination of chaos”, Phys. Usp., 53:12 (2010), 1257–1280  mathnet  crossref  crossref  isi  elib
    25. V. Yu. Protasov, “Invariant Functionals for Random Matrices”, Funct. Anal. Appl., 44:3 (2010), 230–233  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    26. V. Yu. Protasov, “Invariant functions for the Lyapunov exponents of random matrices”, Sb. Math., 202:1 (2011), 101–126  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    27. V. P. Budaev, S. P. Savin, L. M. Zelenyi, “Investigation of intermittency and generalized self-similarity of turbulent boundary layers in laboratory and magnetospheric plasmas: towards a quantitative definition of plasma transport features”, Phys. Usp., 54:9 (2011), 875–918  mathnet  crossref  crossref  adsnasa  isi
    28. Shilov I.O., “Attraktornyi podkhod k izucheniyu prostranstvenno-vremennoi izmenchivosti gidrometeorologicheskikh protsessov i polei”, Izvestiya russkogo geograficheskogo obschestva, 143:1 (2011), 49–67  elib
    29. M. E. Lipatov, “Classification of Cocycles over Ergodic Automorphisms with Values in the Lorentz Group and Recurrence of Cocycles”, Math. Notes, 93:6 (2013), 850–857  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    30. V. Yu. Protasov, “Asymptotics of Products of Nonnegative Random Matrices”, Funct. Anal. Appl., 47:2 (2013), 138–147  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
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    38. V. E. Goryunov, M. M. Preobrazhenskaya, “Kvaziustoichivost sosuschestvuyuschikh attraktorov neirodinamicheskoi modeli s zapazdyvaniem”, Materialy Voronezhskoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy». 28 yanvarya–2 fevralya 2019 g. Chast 4, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 173, VINITI RAN, M., 2019, 26–47  mathnet  crossref
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