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Generalized zeta-functions for axiom A basic sets. (English) Zbl 0316.58016

MSC:
37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory, local dynamics
37D99 Dynamical systems with hyperbolic behavior
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[1] Huzihiro Araki, Gibbs states of a one dimensional quantum lattice, Comm. Math. Phys. 14 (1969), 120 – 157. · Zbl 0199.28001
[2] Rufus Bowen, Markov partitions for Axiom \? diffeomorphisms, Amer. J. Math. 92 (1970), 725 – 747. · Zbl 0208.25901 · doi:10.2307/2373370 · doi.org
[3] Rufus Bowen, Symbolic dynamics for hyperbolic flows, Amer. J. Math. 95 (1973), 429 – 460. · Zbl 0282.58009 · doi:10.2307/2373793 · doi.org
[4] Rufus Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Lecture Notes in Mathematics, Vol. 470, Springer-Verlag, Berlin-New York, 1975. · Zbl 0308.28010
[5] Rufus Bowen and David Ruelle, The ergodic theory of Axiom A flows, Invent. Math. 29 (1975), no. 3, 181 – 202. · Zbl 0311.58010 · doi:10.1007/BF01389848 · doi.org
[6] Anthony Manning, Axiom \? diffeomorphisms have rational zeta functions, Bull. London Math. Soc. 3 (1971), 215 – 220. · Zbl 0219.58007 · doi:10.1112/blms/3.2.215 · doi.org
[7] D. Ruelle, Statistical mechanics of a one-dimensional lattice gas, Comm. Math. Phys. 9 (1968), 267 – 278. · Zbl 0165.29102
[8] David Ruelle, Statistical mechanics on a compact set with \?^\? action satisfying expansiveness and specification, Bull. Amer. Math. Soc. 78 (1972), 988 – 991. · Zbl 0255.28015
[9] David Ruelle, A measure associated with axiom-A attractors, Amer. J. Math. 98 (1976), no. 3, 619 – 654. · Zbl 0355.58010 · doi:10.2307/2373810 · doi.org
[10] D. Ruelle, Notes on classical statistical mechanics (to appear). · Zbl 0154.46503
[11] Ja. G. Sinaĭ, Construction of Markov partitionings, Funkcional. Anal. i Priložen. 2 (1968), no. 3, 70 – 80 (Loose errata) (Russian).
[12] Ja. G. Sinaĭ, Gibbs measures in ergodic theory, Uspehi Mat. Nauk 27 (1972), no. 4(166), 21 – 64 (Russian).
[13] S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747 – 817. · Zbl 0202.55202
[14] Peter Walters, A variational principle for the pressure of continuous transformations, Amer. J. Math. 97 (1975), no. 4, 937 – 971. · Zbl 0318.28007 · doi:10.2307/2373682 · doi.org
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