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References
Arnold, V.I., Avez, A.: Ergodic problems of classical mechanics. New York: Benjamin 1968
Bowen, R.: Equilibrium states and the ergodic theory of Anosov diffeomorphisms. S.L.N.470, Berlin-Heidelberg-New York: Springer 1975
Bowen, R.: On Axiom A diffeomorphisms. Am. Math. Soc. Regional Conf. Proc. No.35, Providence 1978
Bowen, R.: Symbolic dynamics for hyperbolic flows. Am J. Math.95, 429–459 (1973)
Bowen, R.: Periodic orbits for hyperbolic flows. Am. J. Math.94, 1–30 (1972)
Bowen, R., Ruelle, D.: The ergodic theory of Axiom A flows. Invent. Math.29, 181–202 (1975)
Bowen, R., Walters, P.: Expansive one-parameter flows. J. Differ. Equations12, 180–193 (1972)
Bowen, R., Series, C.: Markov maps associated with Fuchsian groups. Publ. Math. Inst. Hautes Etud. Sci.50, 153–170 (1979)
Collet, P., Epstein, H., Gallavotti, G.: Perturbations of geodesic flows on surfaces of constant negative curvature and their mixing properties. Commun. Math. Phys.95, 61–112 (1984)
Cornfeld, I.P., Fomin, S.V., Sinai, Y.G.: Ergodic Theory. Berlin-Heidelberg-New York: Springer 1982
Fomin, S.V., Gelfand, I.M.: Geodesic flows on manifolds of constant negative curvature. Transl. Am. Math. Soc.1, 49–65 (1955)
Gallavotti, G.: Funzioni zeta ed insiemi basilar. Accad. Lincei. Rend. Sc. fismat. e mat.61, 309–317 (1976)
Hardy, G.H., Wright, E.M.: An introduction to the theory of numbers. Oxford: O.U.P. 1983
Hejhal, D.A.: The Selberg trace formula and the Riemann zeta function. Duke Math. J.43 441–482 (1976)
Katznelson, Y.: An introduction to harmonic analysis. Dover: New York 1976
Manning, A.: Axiom A diffeomorphisms have rational zeta functions. Bull. London Math. Soc.3, 215–220 (1971)
Parry, W.: Intrinsic Markov Chains. Trans. Am. Math. Soc.112, 55–65 (1964)
Parry, W.: Topics in Ergodic theory. Cambridge: C.U.P. 1981
Parry, W., Pollicott, M.: An analogue of the prime number theorem for closed orbits of Axiom A flows. Ann. Math.118, 573–591 (1983)
Pollicott, M.: Meromorphic extensions of generalised zeta functions (Preprint)
Pollicott, M.: Asymptotic distribution of closed geodesics (To appear in Isr. J. Math.)
Ruelle, D.: Flows which do not exponentially mix. C.R. Acad. Sci. Paris296, 191–194 (1983)
Ruelle, D.: Thermodynamic formalism. Reading: Addison-Weley 1978
Ruelle, D.: Zeta functions for expanding maps and Anosov flows. Invent. Math.34, 23L-242 (1976)
Series, C.: Symbolic dynamics for geodesic flows. Acta Math.146, 103–128 (1981)
Schoen, R., Wolpert, S., Yau, S.T.: Geometric bounds on the low eigenvalues of a compact surface. In: Proc. Symp. Pure Math.36 (1980)
Sinai, Y.G.: Gibbs measures in ergodic. theory. Russ. Math. Surv.27, 21–69 (1972)
Smale, S.: Differentiable dynamical systems. Bull. Am. Math. Soc.73, 747–817 (1967)
Tuncel, S.: Conditional pressure and coding. Isr. J. Math.39, 101–112 (1981)
Venkov, A.B.: Spectral theory of automorphic functions, the selberg zeta function, and some problems of analytic number theory and mathematical physics. Russ. Math. Surv.34, 79–153 (1979)
Walters, P.: A variational principle for the pressure of continuous transformations. Am. J. Math.97, 937–971 (1976)
Walters, P.: An introduction to ergodic theory. G.T.M.79, Berlin-Heidelberg-New York: Springer 1981
Walters, P.: Ruelle's operator theorem andg-measures. Trans. Am. Math. Soc.214, 375–387 (1975)
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Pollicott, M. On the rate of mixing of Axiom A flows. Invent Math 81, 413–426 (1985). https://doi.org/10.1007/BF01388579
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DOI: https://doi.org/10.1007/BF01388579