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Investigation of invariants of a many-particle system by the method of projection operators

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Literature Cited

  1. N. B. Bogolyubov, Some Statistical Methods in Mathematical Physics [in Russian], Izd-vo Akad. Nauk UkrSSR, L'vov (1945).

    Google Scholar 

  2. N. N. Bogolyubov, “Problems of a dynamical theory in statistical physics”, in: Studies in Statistical Mechanics, Vol. 1 (ed. J. de Boer and G. E. Uhlenbeck), North-Holland, Amsterdam (1962).

    Google Scholar 

  3. N. M. Krylov and N. N. Bogolyubov, Application of the Methods of Nonlinear Mechanics to the Theory of Stationary Oscillations [in Russian], Izd-vo VUAN, Kiev (1934).

    Google Scholar 

  4. N. N. Bogolyubov and Y. A. Mitropolsky, Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordon and Breach, New York (1962).

    Google Scholar 

  5. Yu. A. Mitropol'skii and O. B. Lykova, Integral Manifolds in Nonlinear Mechanics [in Russian], Nauka (1973).

  6. M. A. Krasnosel'skii, G. M. Vainikko, P. P. Zabreiko, Ya. B. Rutitskii, and V. Ya. Stetsenko, Approximate Solution of Operator Equations [in Russian], Nauka (1969).

  7. I. Prigogine, C. George, and F. Henin, Proc. Nat. Acad. Sci.,65, 789 (1970).

    Google Scholar 

  8. R. Balescu, P. Clavin, P. Mandel, and J. Turner, Bull. A. Roy. Belgique Cl. Sci.,55, 1055 (1970).

    Google Scholar 

  9. A. P. Grecos, Physics,51, 50 (1971).

    Google Scholar 

  10. A. P. Grecos and I. Prigogine, Physica,59, 77 (1972).

    Google Scholar 

  11. K. O. Friedrichs, Perturbation of Spectra in Hilbert Space, Providence, R. I. (1965).

  12. W. J. Caspers, Physica,26, 778 (1960); Theory of Spin Relaxation, Interscience, New York (1964).

    Google Scholar 

  13. J. A. Tjon, Physica,30, 1, 1341 (1964); Phys. Rev.,143, 259 (1966).

    Google Scholar 

  14. S. Sauermann, Physica,32, 2017 (1966).

    Google Scholar 

  15. R. H. Terwiel and P. Mazur, Physica,32, 1813 (1966);36, 289 (1967).

    Google Scholar 

  16. R. Shimizu, J. Phys. Soc. Japan,32, 598 (1972).

    Google Scholar 

  17. P. Mazur, Physica,43, 533 (1969).

    Google Scholar 

  18. M. Suzuki, Physica,51, 277 (1971).

    Google Scholar 

  19. T. Shimizu, Progr. Theor. Phys.,47, 1181 (1972).

    Google Scholar 

  20. R. Zwanzig, J. Chem. Phys.,33, 1338 (1960); Phys. Rev.,124, 983 (1961); H. Mori, Progr. Theor. Phys.,34, 399 (1965);33, 423 (1965); K. Kawasaki, Ann. Phys.,61, 1 (1970); T. Shimizu, J. Phys. Soc. Japan,28, 811, 827, 790, 1088 (1970).

    Google Scholar 

  21. D. N. Zubarev and V. P. Kalashnikov, Physica,56, 345 (1971); D. N. Zubarev and M. Yu. Novikov, Teor. Mat. Fiz.,13, 406 (1972); M. Yu. Novikov, Teor. Mat. Fiz.,16, 394 (1973).

    Google Scholar 

  22. R. Balescu, Physica,38, 98, 118 (1968);54, 477 (1971); L. Lugiato, Physica,49, 49 (1970);44, 337 (1969); L. Lanz and F. Ramella, Physica,44, 499 (1969);45, 104, (1970); P. Resibois, J. Brocas, and C. Decan, J. Math. Phys.,10, 964 (1969).

    Google Scholar 

  23. R. M. Yul'met'ev, Ukr. Fiz. Zh.,12, 24 (1967);16, 1524 (1971);17, 761 (1972);15, 881 (1970);14, 1898 (1969); Izv. Vuzov, Fizika, No. 9, 19 (1968).

    Google Scholar 

  24. R. M. Yul'met'ev, Phys. Lett.,43A, 115 (1973); Izv. Akad. Nauk SSSR, Ser. Fiz.,37, 2235 (1973); Phys. Stat. Sol.,59B, 677 (1973).

    Google Scholar 

  25. F. Rösler and K. L. Drechsler, Phys. Lett.,27A, 231 (1968).

    Google Scholar 

  26. R. Peierls, Proc. Roy. Soc. London,A333, 157 (1973).

    Google Scholar 

  27. I. Z. Fisher, Statistical Theory of Liquids, Chicago (1964).

  28. R. M. Yul'met'ev, Izv. Vuzov, Fizika, No. 9, 68 (1970).

    Google Scholar 

  29. L. D. Landau, Zh. Éksp. Teor. Fiz.,7, 293 (1937).

    Google Scholar 

  30. K. P. Gurov, Fundamentals of Kinetic Theory (Bogolyubov's Method) [in Russian], Nauka (1966).

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Kazan State Pedogogical Institute. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 20, No. 3, pp. 413–425, September, 1974.

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Yul'met'ev, R.M. Investigation of invariants of a many-particle system by the method of projection operators. Theor Math Phys 20, 914–922 (1974). https://doi.org/10.1007/BF01040172

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  • DOI: https://doi.org/10.1007/BF01040172

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