Zeta functions and statistical mechanics
International conference on dynamical systems in mathematical physics, Astérisque, no. 40 (1976), pp. 167-176.
@incollection{AST_1976__40__167_0,
author = {Ruelle, D.},
title = {Zeta functions and statistical mechanics},
booktitle = {International conference on dynamical systems in mathematical physics},
author = {Collectif},
series = {Ast\'erisque},
publisher = {Soci\'et\'e math\'ematique de France},
number = {40},
year = {1976},
zbl = {0382.58018},
mrnumber = {458497},
language = {en},
url = {http://www.numdam.org/item/AST_1976__40__167_0/}
}
TY  - CHAP
AU  - Ruelle, D.
TI  - Zeta functions and statistical mechanics
BT  - International conference on dynamical systems in mathematical physics
AU  - Collectif
T3  - Astérisque
PY  - 1976
DA  - 1976///
IS  - 40
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_1976__40__167_0/
UR  - https://zbmath.org/?q=an%3A0382.58018
UR  - https://www.ams.org/mathscinet-getitem?mr=458497
LA  - en
ID  - AST_1976__40__167_0
ER  - 
%0 Book Section
%A Ruelle, D.
%T Zeta functions and statistical mechanics
%B International conference on dynamical systems in mathematical physics
%A Collectif
%S Astérisque
%D 1976
%N 40
%I Société mathématique de France
%G en
%F AST_1976__40__167_0
Ruelle, D. Zeta functions and statistical mechanics, in International conference on dynamical systems in mathematical physics, Astérisque, no. 40 (1976), pp. 167-176. http://www.numdam.org/item/AST_1976__40__167_0/

[1] B. Riemann. Uber die Anzahl der Primzahl en unterhalb einer gegebenen Grösse.

[2] A. Weil. Numbers of solutions of equations in finite fields. Bull. Am. Math. Soc. 55, (1949), 497-508 | DOI | MR | Zbl

[3] P. Deligne. La conjecture de Weil I. IHES Publ. math. 43, (1974), 273-307 | DOI | EuDML | MR | Zbl

[4] M. Artin and B. Mazur. On periodic points. Ann. of Math. 81, (1965), 82-99 | DOI | MR | Zbl

[5] S. Smale. Differentiable dynamical systems. Bull. A.M.S. 73, (1967), 747-817 | DOI | MR | Zbl

[6] A. Selberg. Harmonic analysis and discontinuous groups in weakly symmetric Riemann spaces with applications to Dirichlet series. J. Indian Math. Soc. 20, (1956), 47-87 | MR | Zbl

[7] T. D. Lee and C. N. Yang. Statistical theory of Equations of state and phase transitions, II, Lattice gas and Ising model. Phys. Rev. 87, 410-419, (1952) | DOI | MR | Zbl

[8] Ch. Newman. Classifying general Ising models. Lecture given at the International Colloquium on Mathematical Methods in Quantum Field Theory. Marseille, June 1975

[9] J. Guckenheimer. Axiom $A+$ no cycles $⇒{\zeta }_{f}\left(t\right)$ rational. Bull. A.M.S. 76, (1970), 592-594 | DOI | MR | Zbl

[10] A. Manning. Axiom A diffeomorphisms have rational zeta functions. Bull. London Math. Soc. 3, (1971), 215-220 | DOI | MR | Zbl

[11] M. Atiyah and R. Bott. Notes on the Lefshetz fixed point theorem for elliptic complexes. Harvard University. Fall 1964 | Zbl

[12] R. Bowen. Markov partitions for Axiom A diffeomorphisms. Amer. J. Math. 92, (1970), 725-747 | DOI | MR | Zbl

R. Bowen. Markov partitions and minimal sets for Axiom A diffeomorphisms. Amer. J. Math. 92, (1970), 907-918. | DOI | MR | Zbl

[13] Ia. G. Sinai. Markov partitions and $C$-diffeomorphisms. Funkts. Analiz Pril. 2 n° 1, (1968), 64-89 ; English translation Funct. Anal. Appl. 2, (1968), 61-82. | MR | Zbl

Ia. G. Sinai. Construction of Markov partitions. Funkts. Analiz Pril. 2, n° 3, (1968), 70-80 ; English translation Funct Anal. Appl. 2, (1968), 245-253 | Zbl

[14] R. Bowen and O. E. Lanford Iii. Zeta functions of restrictions of the shift map. Proc. Symp. pure math. 14, (1970), 43-49 | DOI | MR | Zbl

[15] Ia. G. Sinai. Gibbsian measures in ergodic theory. Uspekhi mat. Nauk 27 n° 4, (1972), 21-64. English translation Russian math. Surveys 166, (1972), 21-69. | MR | Zbl

[16] D. Ruelle. Generalized zeta-functions for Axiom A basic sets. Bull. Amer. Math. Soc. 82, 153-156 (1976) | DOI | MR | Zbl

[17] P. Walters. A variational principle for the pressure of continuous transformations. Amer. J. Math. To appear | MR | Zbl

[18] R. Bowen. Symbolic dynamics for hyperbolic flows. Amer. J. Math. 95, (1973), 429-460 | DOI | MR | Zbl

[19] A. Grothendieck. Produits tensoriels topologiques et espaces nucléaires. Mémoirs of the Amer. math. Soc. 16, Providence, R.I., (1955) | MR | Zbl

A. Grothendieck. La théorie de Fredholm. Bull. Soc. math. France, 84, (1956), 319-384. | DOI | EuDML | MR | Zbl

[20] D. Ruelle. Zeta functions for expanding maps and Anosov flows. Inventiones Math. 34, 231-242 (1976) | DOI | EuDML | MR | Zbl