Advertisement

Functional Analysis and Its Applications

, Volume 26, Issue 3, pp 155–169 | Cite as

Mixing for some classes of special flows over rotations of the circle

  • Ya. G. Sinai
  • K. M. Khanin
Article

Keywords

Functional Analysis Special Flow 
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.

References

  1. 1.
    V. I. Arnol'd, “Topological and ergodic properties of closed 1-forms with noncommensurable periods,” Funkts. Anal. Prilozhen.,25, No. 2, 1–12 (1991).Google Scholar
  2. 2.
    I. P. Kornfeld, Ya. G. Sinai, and S. V. Fomin, Ergodic Theory [in Russian], Nauka, Moscow (1980).Google Scholar
  3. 3.
    A. N. Kolmogorov, “On dynamic systems with integral invariant on a torus,” Dokl. Akad. Nauk SSSR,93, No. 5, 763–766 (1953).Google Scholar
  4. 4.
    M. D. Shklover, “On dynamic systems with continuous spectrum on a torus,” Izv. Vyssh. Uchebn. Zaved. Ser. Mat.,10, 113–124 (1967).Google Scholar
  5. 5.
    J. von Neumann, “Zur Operatorenmethode in der klassischen Mechanik,” Ann. of Math. (2),33, No. 3, 587–642 (1932).Google Scholar
  6. 6.
    A. V. Kochergin, “Non-degenerate saddle points and absence of mixing,” Mat. Zametki,19, No. 3, 453–468 (1976).Google Scholar
  7. 7.
    K. M. Khanin and Ya. G. Sinai, “A new proof of M. Hermann's theorem,” Comm. Math. Phys.,112, 89–101 (1987).Google Scholar
  8. 8.
    Ya. G. Sinai and K. M. Khanin, “Smoothness of conjugacies of diffeomorphisms of the circle with rotations,” Usp. Mat. Nauk,44, No. 1, 57–82 (1989).Google Scholar
  9. 9.
    A. Ya. Khinchin, Continued Fractions [in Russian], Nauka, Moscow (1978).Google Scholar

Copyright information

© Plenum Publishing Corporation 1992

Authors and Affiliations

  • Ya. G. Sinai
  • K. M. Khanin

There are no affiliations available

Personalised recommendations