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Dokl. Akad. Nauk SSSR, 1958, Volume 119, Number 5, Pages 861–864 (Mi dan22922)  

This article is cited in 28 scientific papers (total in 29 papers)


A new metric invariant of transient dynamical systems and automorphisms in Lebesgue spaces

A. N. Kolmogorov

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Received: 21.01.1958

Citation: A. N. Kolmogorov, “A new metric invariant of transient dynamical systems and automorphisms in Lebesgue spaces”, Dokl. Akad. Nauk SSSR, 119:5 (1958), 861–864

Citation in format AMSBIB
\by A.~N.~Kolmogorov
\paper A new metric invariant of transient dynamical systems and automorphisms in Lebesgue spaces
\jour Dokl. Akad. Nauk SSSR
\yr 1958
\vol 119
\issue 5
\pages 861--864

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    This publication is cited in the following articles:
    1. V. A. Rokhlin, “Lectures on the entropy theory of measure-preserving transformations”, Russian Math. Surveys, 22:5 (1967), 1–52  mathnet  crossref  mathscinet  zmath
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    3. A. K. Zvonkin, L. A. Levin, “The complexity of finite objects and the development of the concepts of information and randomness by means of the theory of algorithms”, Russian Math. Surveys, 25:6 (1970), 83–124  mathnet  crossref  mathscinet  zmath
    4. K. L. Volkovysskii, Ya. G. Sinai, “Ergodic properties of an ideal gas with an infinite number of degrees of freedom”, Funct. Anal. Appl., 5:3 (1971), 185–187  mathnet  crossref  mathscinet  zmath
    5. E. I. Dinaburg, “On the relations among various entropy characteristics of dynamical systems”, Math. USSR-Izv., 5:2 (1971), 337–378  mathnet  crossref  mathscinet  zmath
    6. N. M. Pukhov, D. S. Chernavskii, “On phase instability in the case of scattering by a random potential”, Theoret. and Math. Phys., 7:2 (1971), 487–494  mathnet  crossref
    7. Ya. G. Sinai, “Ergodic properties of a gas of one-dimensional hard rods with an infinite number of degrees of freedom”, Funct. Anal. Appl., 6:1 (1972), 35–43  mathnet  crossref  mathscinet  zmath
    8. B. M. Gurevich, Ya. G. Sinai, Yu. M. Sukhov, “On invariant measures of dynamical systems of one-dimensional statistical mechanics”, Russian Math. Surveys, 28:5 (1973), 49–86  mathnet  crossref  mathscinet  zmath
    9. D. L. Shepelyanskii, “Dynamical stochasticity in nonlinear quantum systems”, Theoret. and Math. Phys., 49:1 (1981), 925–928  mathnet  crossref  mathscinet  isi
    10. V. M. Tikhomirov, “Widths and entropy”, Russian Math. Surveys, 38:4 (1983), 101–111  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    11. R. V. Plykin, “On the geometry of hyperbolic attractors of smooth cascades”, Russian Math. Surveys, 39:6 (1984), 85–131  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    12. O. N. Ageev, “Dynamical systems with an even-mulriplicity Lebesgue component in the spectrum”, Math. USSR-Sb., 64:2 (1989), 305–317  mathnet  crossref  mathscinet  zmath
    13. 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
    14. Ya. G. Sinai, “Finite-dimensional randomness”, Russian Math. Surveys, 46:3 (1991), 177–190  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    15. S. V. Savchenko, “Special Flows Constructed From Countable Topological Markov Chains”, Funct. Anal. Appl., 32:1 (1998), 32–41  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    16. A. M. Vershik, “Dynamic theory of growth in groups: Entropy, boundaries, examples”, Russian Math. Surveys, 55:4 (2000), 667–733  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    17. L. M. Zelenyi, A. V. Milovanov, “Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics”, Phys. Usp., 47:8 (2004), 749–788  mathnet  crossref  crossref  isi
    18. G. G. Amosov, “On Markov perturbations of quantum random problems with stationary increments”, Theory Probab. Appl., 50:4 (2006), 650–658  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    19. A. Yu. Loskutov, “Dynamical chaos: systems of classical mechanics”, Phys. Usp., 50:9 (2007), 939–964  mathnet  crossref  crossref  adsnasa  isi  elib
    20. B. R. Andriesky, A. S. Matveev, A. L. Fradkov, “Control and estimation under information constraints: toward a unified theory of control, computation and communications”, Autom. Remote Control, 71:4 (2010), 572–633  mathnet  crossref  mathscinet  zmath  isi  elib
    21. A. I. Bufetov, B. M. Gurevich, K. M. Khanin, F. Cellarosi, “The Abel Prize award to Ya. G. Sinai”, Russian Math. Surveys, 69:5 (2014), 931–956  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    22. P. B. Zatitskii, “On a Scaling Entropy Sequence of a Dynamical System”, Funct. Anal. Appl., 48:4 (2014), 291–294  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    23. O. G. Bakunin, “Stochastic instability and turbulent transport. Characteristic scales, increments, and diffusion coefficients”, Phys. Usp., 58:3 (2015), 252–285  mathnet  crossref  crossref  adsnasa  isi  elib
    24. P. B. Zatitskiy, “Scaling entropy sequence: invariance and examples”, J. Math. Sci. (N. Y.), 209:6 (2015), 890–909  mathnet  crossref
    25. D. Z. Arov, “To the history of the appearance of the notion of $\epsilon$-entropy of an authomorphism of a Lebesque space and $(\varepsilon,T)$-entropy of a dynamical system with continuous time”, J. Math. Sci. (N. Y.), 215:6 (2016), 677–692  mathnet  crossref  mathscinet
    26. B. M. Gurevich, “Toward the history of dynamical entropy: comparing two definitions”, J. Math. Sci. (N. Y.), 215:6 (2016), 693–699  mathnet  crossref  mathscinet
    27. G. K. Savvidi, “Anosov C-systems and random number generators”, Theoret. and Math. Phys., 188:2 (2016), 1155–1171  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    28. A. M. Vershik, “The theory of filtrations of subalgebras, standardness, and independence”, Russian Math. Surveys, 72:2 (2017), 257–333  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    29. L. S. Efremova, E. N. Makhrova, “Odnomernye dinamicheskie sistemy”, UMN, 76:5(461) (2021), 81–146  mathnet  crossref
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