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On local ergodicity in hyperbolic systems with singularities

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References

  1. Ya. G. Sinai, “Ergodic properties of the Lorentz gas,” Funkts. Anal. Prilozhen.,13, No. 4, 46–59 (1979).

    Google Scholar 

  2. Ya. G. Sinai and N. I. Chernov, “Ergodic properties of some systems of 2-dimensional disks and 3-dimensional sphere,” Usp. Mat. Nauk,42, No. 3, 153–174 (1987).

    Google Scholar 

  3. A. Krámli, N. Simányi, and D. Szász, “Three billiard balls on thev-dimensional torus is aK-flow,” Ann. of Math.,133, 37–72 (1991).

    Google Scholar 

  4. L. A. Bunimovich, C. Liverani, A. Pellegrinotti, and Yu. M. Sukhov, “Ergodic systems ofN balls in a billiard table,” Preprint (1991).

  5. V. Donnay and C. Liverani, “Potentials on the two-torus for which the Hamiltonian flow is ergodic,” Comm. Math. Phys.,135, No. 2, 267–302 (1991).

    Google Scholar 

  6. R. Markarian, “The fundamental theorem of Sinai—Chernov for dynamical systems with singularities,” Preprint (1991).

  7. A. Krámli, N. Simányi, and D. Szász, “A “transversal” fundamental theorem for semi-dispersing billiards,” Comm. Math. Phys.,129, No. 3, 535–560 (1990).

    Google Scholar 

  8. M. Wojtkowski, “A system of one-dimensional balls with gravity,” Comm. Math. Phys.,126, No. 3, 507–533 (1990).

    Google Scholar 

  9. M. Wojtkowski, “The system of one-dimensional balls in an external field,” Comm. Math. Phys.,127, No. 2, 425–432 (1990).

    Google Scholar 

  10. N. I. Chernov, “The ergodicity of a Hamiltonian system of two particles in an external field,” Physica D (to appear).

  11. A. Katok and J.-M. Strelcyn, “Smooth maps with singularities: invariant manifolds, entropy and billiards,” Lecture Notes in Math.,1222, Springer—Verlag (1987).

  12. V. I. Oseledets, “A multiplicative ergodic theorem: characteristic Lyapunov exponents of dynamical systems,” Trudy Mosk. Mat. Obshch.,19, 179–210 (1968).

    Google Scholar 

  13. M. Wojtkowski, “Invariant families of cones and Lyapunov exponents,” Ergod. Theory Dyn. Syst.,5, No. 1, 145–161 (1985).

    Google Scholar 

  14. Dynamical systems II, Encyclopedia of Mathematical Sciences, Vol. 2, Springer—Verlag, Berlin (1989).

    Google Scholar 

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United Institute of Nuclear Research. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 27, No. 1, pp. 60–64, January–March, 1993.

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Chernov, N.I. On local ergodicity in hyperbolic systems with singularities. Funct Anal Its Appl 27, 51–54 (1993). https://doi.org/10.1007/BF01768668

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