Journal of Mathematical Sciences

, Volume 95, Issue 5, pp 2564–2575 | Cite as

Ergodic properties of the Belykh map

  • E. A. Sataev


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.


  1. 1.
    V. S. Afraimovich, N. I. Chernov, and E. A. Sataev,Statistical properties of 2-D generalized hyperbolic attractors, preprint CDSNS93-143, Georgia Institute of Technology (to appear).Google Scholar
  2. 2.
    V. N. Belykh, “Models of discrete systems of phase synchronization,” in: V. V. Shakhildyan and L. N. Belyustina, eds.,Systems of Phase Synchronization [in Russian], Radio i Svyaz', (1982), pp. 161–216.Google Scholar
  3. 3.
    R. Bowen, “Equilibrium states and the ergodic theory of Anosov diffeomorphisms,”Lect. Notes Math.,470 (1975).Google Scholar
  4. 4.
    L. A. Bunimovich and Ya. G. Sinai, “Stochasticity of the attractor in the Lorenz model,” in:Nonlinear Waves (Proc. Winter School, Moscow), Nauka, Moscow (1980), pp. 212–226.Google Scholar
  5. 5.
    P. Collet and Y. Levy, “Ergodic properties of the Lozi mappings,”Commun. Math. Phys.,93, No. 4, 461–482 (1984).Google Scholar
  6. 6.
    R. Lozi, “Un attracteur ètrange du type attracteur de Henon,”J. Phis.,39, 9–10, (1978)Google Scholar
  7. 7.
    M. Misiurewicz, “Strange attractors for the Lozi mappings,” in: Helleman, ed.Nonlinear Dynamics, New York (1980), pp. 348–358.Google Scholar
  8. 8.
    A. B. Katok and J.-M. Strelcyn, “Invariant manifolds, entropy and billiards. Smooth maps with singularities,”Lect. Notes Math.,1222, 1–212 (1986).Google Scholar
  9. 9.
    Ya. B. Pesin, “Characteristic Lyapunov exponents and smooth ergodic theory,”Russian Math. Surveys,32, 55–114 (1977).Google Scholar
  10. 10.
    Ya. B. Pesin, “Ergodic properties and dimensionlike characteristics of strange attractors that are close to hyperbolic,”Proc. Int. Cong. Math. (1986).Google Scholar
  11. 11.
    Ya. B. Pesin, “Dynamical systems with generalized hyperbolic attractors: hyperbolic, ergodic and topological properties,”Ergod. Theory Dyn. Sys.,12, 123–151 (1992).Google Scholar
  12. 12.
    D. Ruelle, “Ergodic theory of differential dynamical systems,”Publ. Math. IHES,50, 27–58 (1979).Google Scholar
  13. 13.
    E. A. Sataev, “Invariant measures for hyperbolic maps with singularities,”Russian Math. Surveys,47, No. 1, 191–251 (1992).Google Scholar
  14. 14.
    E. A. Sataev, “Gibbs measures for one-dimensional attractors of hyperbolic maps with singularities,”Izv. Akad. Nauk Rossii, Ser. Mat.,56, No. 6, 1328–1344 (1992).Google Scholar
  15. 15.
    Ya. G. Sinai, “Gibbs measures in ergodic theory,”Russian Math. Surveys,27, No. 4, 21–64.Google Scholar
  16. 16.
    L.-S. Young, “Bowen-Ruelle measures for certain piecewise hyperbolic maps,”Trans. Amer. Math. Soc.,287, No. 1, 41–48 (1985).Google Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • E. A. Sataev

There are no affiliations available

Personalised recommendations