Functional Analysis and Its Applications

, Volume 32, Issue 1, pp 32–41

Special flows constructed from countable topological Markov chains

  • S. V. Savchenko
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References

  1. 1.
    L. M. Abramov, “On the entropy of a flow,” Dokl. Akad. Nauk SSSR,128, No. 5, 873–875 (1959); English transl. in Amer. Math. Soc. Transl., Ser. 2,49, 167–170 (1966).MATHMathSciNetGoogle Scholar
  2. 2.
    W. Parry W. and M. Pollicott, “Zeta functions and the periodic orbit structure of hyperbolic dynamics,” Astérisque,187–188 (1990).Google Scholar
  3. 3.
    U. Krengel, “Entropy of conservative transformations” Z. Wahrscheinlichkeitstheorie verw. Gebiete,7, 161–181 (1967).MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    S. Smale, “Differentiable dynamical systems,” Usp. Mat. Nauk,25, No. 1, 113–185 (1970).MathSciNetGoogle Scholar
  5. 5.
    R. Bowen and D. Ruelle, “The ergodic theory of Axiom A flows,” Invent. Math.29, 181–202 (1975).MATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    L. A. Bunimovich, Ya. G. Sinai, and N. I. Chernov, “Markov partitions for two-dimensional hyperbolic billiards,” Usp. Mat. Nauk,45, No. 3, 97–134 (1990).MATHMathSciNetGoogle Scholar
  7. 7.
    Ya. G. Sinai, Introduction to Ergodic Theory, BSM series No. 1, Fasis, Moscow, 1996.MATHGoogle Scholar
  8. 8.
    D. Ruelle, “Generalized zeta-functions for axiom A basic sets,” Bull. Amer. Math. Soc.,82, 153–156 (1976).MATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    W. Parry and M. Pollicott, “An analogue of the prime number theorem and closed orbits of Axiom A flows,” Ann. Math.,118, 573–591 (1983).MATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    H. Huber, “Zur analytischen Theorie hyperbolischer Raum formen und Bewegungsgruppen,” II, Math. Ann.,142, 385–398 (1961).MATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    S. V. Savchenko, “Periodic points of countable topological Markov chains,” Mat. Sb.,186, No. 10, 103–140 (1995); English transl. in Russian Acad. Sci. Sb. Math.,186, No. 10, 1493–1529 (1995).MATHMathSciNetGoogle Scholar
  12. 12.
    R. Bowen and P. Walters, “Expansive one-parameter flows,” J. Differential Equations,12, 180–193 (1972).MATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    S. V. Savchenko, “Equilibrium states with incomplete supports and periodic orbits,” Mat. Zametki,59, No. 2, 230–253 (1996); English transl. in Math. Notes,59, No. 2, 163–179 (1996).MATHMathSciNetGoogle Scholar
  14. 14.
    W. Parry, “Ergodic and spectral analysis of certain infinite measure preserving transformations,” Proc. Amer. Math. Soc.,16, 960–966 (1965).MATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    L. Sucheston, “A note on conservative transformations and the recurrence theorem,” Amer. J. Math.,79, 444–447 (1957).MATHMathSciNetCrossRefGoogle Scholar
  16. 16.
    A. N. Kolmogorov, “A new metric invariant of transitive dynamical systems and automorphisms of Lebesgue spaces,” Dokl. Akad. Nauk SSSR,119, No. 5, 861–864 (1958).MATHMathSciNetGoogle Scholar
  17. 17.
    V. A. Rokhlin, “Lectures on the entropy theory of transformations with an invariant measure,” Usp. Mat. Nauk,22, No. 5, 3–56 (1967).MATHMathSciNetGoogle Scholar
  18. 18.
    L. M. Abramov, “On the entropy of the derived automorphism,” Dokl. Akad Nauk SSSR,128, No. 4, 647–650 (1959).MATHMathSciNetGoogle Scholar
  19. 19.
    B. M. Gurevich, “A variational characterization of one-dimensional countable state Gibbs random fields,” Z. Wahrscheinlichkeitstheorie verw. Gebiete,68, 205–242 (1984).MATHMathSciNetCrossRefGoogle Scholar

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© Plenum Publishing Corporation 1998

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  • S. V. Savchenko

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