Advertisement

Functional Analysis and Its Applications

, Volume 13, Issue 3, pp 192–202 | Cite as

Ergodic properties of the lorentz gas

  • Ya. G. Sinai
Article

Keywords

Functional Analysis 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    H. A. Lorentz, "The motion of electrons in metallic bodies," Proc. Amst. Acad.,7, 438, 585, 604 (1905).Google Scholar
  2. 2.
    G. Gallavotti, "Divergences and the approach to equilibrium in the Lorentz and windtree models," Phys. Rev.,185, 308–314 (1969).Google Scholar
  3. 3.
    Sh. Goldstein, J. Lebowitz, and M. Aizenman, "Ergodic properties of infinite systems," Lect. Notes Phys.,38, 112–143 (1975).Google Scholar
  4. 4.
    E. H. Hauge, "What one can learn from Lorentz models," Lect. Notes Phys.,31, 337–367 (1974).Google Scholar
  5. 5.
    V. A. Rokhlin, "New progress in the theory of transformations with an invariant measure," Usp. Mat. Nauk,15, No. 4, 3–26 (1960).Google Scholar
  6. 6.
    Ya. G. Sinai, "Dynamical systems with elastic reflections," Usp. Mat. Nauk,25, No. 2, 137–189 (1970).Google Scholar
  7. 7.
    L. A. Bunimovich and Ya. G. Sinai, "On a basic theorem of scattered billiards," Mat. Sb.,90, 407–423 (1973).Google Scholar
  8. 8.
    Ya. G. Sinai, "Development of Krylov's ideas," Afterword to "Works on the Foundations of Statistical Physics," by N. S. Krylov, Princeton University Press (1979), pp. 239–281.Google Scholar
  9. 9.
    E. Hopf, "Statistics of geodesic lines on manifolds of negative curvature," Usp. Mat. Nauk,4, No. 2, 129–170 (1949).Google Scholar
  10. 10.
    D. V. Anosov and Ya. G. Sinai, "Some smooth dynamical systems," Usp. Mat. Nauk,22, No. 5, 107–172 (1967).Google Scholar
  11. 11.
    V. A. Rokhlin, "Lectures on entropy theory of transformations with an invariant measure," Usp. Mat. Nauk,22, No. 5, 3–56 (1967).Google Scholar
  12. 12.
    D. J. Rudolph, "A two-valued step-coding for ergodic flows," Proc. of the Int. Conf. on Dynamical Systems in Math. Phys., Rennes, Sept. 14–21, 1975.Google Scholar
  13. 13.
    B. M. Gurevich, "Improved partitions for ergodic flows," Funkts. Analiz,11, No. 3, 20–23 (1977).Google Scholar
  14. 14.
    V. A. Rokhlin and Ya. G. Sinai, "Construction and properties of invariant measurable partitions," Dokl. Akad. Nauk SSSR,141, No. 5, 1038–1041 (1961).Google Scholar
  15. 15.
    Ya. G. Sinai, "Classical dynamical systems with countable Lebesgue spectrum," Izv. Akad. Nauk SSSR, Ser. Mat.,30, 15–68 (1966).Google Scholar
  16. 16.
    M. I. Brin and Ya. B. Pesin, "Partially hyperbolic dynamical systems," Izv. Akad. Nauk SSSR, Ser. Mat.,38, 170–212 (1974).Google Scholar

Copyright information

© Plenum Publishing Corporation 1980

Authors and Affiliations

  • Ya. G. Sinai

There are no affiliations available

Personalised recommendations