Functional Analysis and Its Applications

, Volume 6, Issue 1, pp 35–43 | Cite as

Ergodic properties of a gas of one-dimensional hard rods with an infinite number of degrees of freedom

  • Ya. G. Sinai


Functional Analysis Infinite Number Ergodic Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    K. L. Volkovysskii and Ya. G. Sinai, "Ergodic properties of an ideal gas with an infinite number of degrees of freedom," Funkts. Analiz.,5, No. 4, 19–21 (1971).Google Scholar
  2. 2.
    A. N. Kolmogorov, "A new metric invariant of transitive automorphisms and flows of Lebesgue spaces," Dokl. Akad. Nauk SSSR,119, No. 5, 861–864 (1958).Google Scholar
  3. 3.
    V. A. Rokhlin, "New progress in the theory of transformations with invariant measure," Uspekhi Mat. Nauk,15, No. 4, 3–26 (1960).Google Scholar
  4. 4.
    Ya. G. Sinai, "Probabilistic ideas in ergodic theory," Proc. Intern. Math. Congress, Stockholm, 540–559 (1963).Google Scholar
  5. 5.
    N. N. Bogolyubov, Problems of Dynamical Theory in Statistical Physics, Gostekhizdat, Moscow (1946).Google Scholar
  6. 6.
    J. Uhlenbeck and J. Ford, Lectures on Statistical Mechanics [Russian translation], Mir, Moscow (1965).Google Scholar
  7. 7.
    D. W. Jepsen, "Dynamics of a simple many-body system of hard rods," J. Math. Phys.,6, 405–414 (1965).Google Scholar
  8. 8.
    J. L. Lebowitz, J. K. Percus, and J. Sykes, "Time evolution of the total distribution function of a one-dimensional system of hard rods," Phys. Rev.,171, No. 1, 224–235 (1968).Google Scholar
  9. 9.
    O. de Pazzis, "Ergodic properties of a semiinfinite hard rods system," Preprint (1971).Google Scholar
  10. 10.
    V. A. Rokhlin, "Selected problems in the metric theory of dynamical systems," Uspekh. Mat. Nauk,4, No. 2, 57–128 (1949).Google Scholar
  11. 11.
    F. Spitzer, "Uniform motion with elastic collision of an infinite particle system," J. Math. Mech.,18, No. 10, 973–989 (1969).Google Scholar
  12. 12.
    T. E. Harris, "Random measures and motions of point processes," Z. Wahrscheindlichkeitstheorie,18, No. 2, 85–115 (1971).Google Scholar

Copyright information

© Consultants Bureau 1972

Authors and Affiliations

  • Ya. G. Sinai

There are no affiliations available

Personalised recommendations