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References
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).
W. Parry W. and M. Pollicott, “Zeta functions and the periodic orbit structure of hyperbolic dynamics,” Astérisque,187–188 (1990).
U. Krengel, “Entropy of conservative transformations” Z. Wahrscheinlichkeitstheorie verw. Gebiete,7, 161–181 (1967).
S. Smale, “Differentiable dynamical systems,” Usp. Mat. Nauk,25, No. 1, 113–185 (1970).
R. Bowen and D. Ruelle, “The ergodic theory of Axiom A flows,” Invent. Math.29, 181–202 (1975).
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).
Ya. G. Sinai, Introduction to Ergodic Theory, BSM series No. 1, Fasis, Moscow, 1996.
D. Ruelle, “Generalized zeta-functions for axiom A basic sets,” Bull. Amer. Math. Soc.,82, 153–156 (1976).
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).
H. Huber, “Zur analytischen Theorie hyperbolischer Raum formen und Bewegungsgruppen,” II, Math. Ann.,142, 385–398 (1961).
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).
R. Bowen and P. Walters, “Expansive one-parameter flows,” J. Differential Equations,12, 180–193 (1972).
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).
W. Parry, “Ergodic and spectral analysis of certain infinite measure preserving transformations,” Proc. Amer. Math. Soc.,16, 960–966 (1965).
L. Sucheston, “A note on conservative transformations and the recurrence theorem,” Amer. J. Math.,79, 444–447 (1957).
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).
V. A. Rokhlin, “Lectures on the entropy theory of transformations with an invariant measure,” Usp. Mat. Nauk,22, No. 5, 3–56 (1967).
L. M. Abramov, “On the entropy of the derived automorphism,” Dokl. Akad Nauk SSSR,128, No. 4, 647–650 (1959).
B. M. Gurevich, “A variational characterization of one-dimensional countable state Gibbs random fields,” Z. Wahrscheinlichkeitstheorie verw. Gebiete,68, 205–242 (1984).
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Supported by INTAS-RFBR grant No. 95-418.
L. D. Landau Institute for Theoretical Physics of the Russian Academy of Sciences. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 32, No. 1, pp. 40–53, January–March, 1998.
Translated by V. E. Nazaikinskii
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Savchenko, S.V. Special flows constructed from countable topological Markov chains. Funct Anal Its Appl 32, 32–41 (1998). https://doi.org/10.1007/BF02465754
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DOI: https://doi.org/10.1007/BF02465754