Zeta Functions and Statistical Mechanics

Ruelle, D.

Ruelle, D.

Publications des séminaires de mathématiques et informatique de Rennes, no. S4 (1975), article no. 22, 10 p.

EuDML

@article{PSMIR_1975___S4_A22_0,
     author = {Ruelle, D.},
     title = {Zeta {Functions} and {Statistical} {Mechanics}},
     journal = {Publications des s\'eminaires de math\'ematiques et informatique de Rennes},
     eid = {22},
     pages = {1--10},
     publisher = {D\'epartement de Math\'ematiques et Informatique, Universit\'e de Rennes},
     number = {S4},
     year = {1975},
     language = {en},
     url = {http://archive.numdam.org/item/PSMIR_1975___S4_A22_0/}
}

TY  - JOUR
AU  - Ruelle, D.
TI  - Zeta Functions and Statistical Mechanics
JO  - Publications des séminaires de mathématiques et informatique de Rennes
PY  - 1975
SP  - 1
EP  - 10
IS  - S4
PB  - Département de Mathématiques et Informatique, Université de Rennes
UR  - http://archive.numdam.org/item/PSMIR_1975___S4_A22_0/
LA  - en
ID  - PSMIR_1975___S4_A22_0
ER  -

%0 Journal Article
%A Ruelle, D.
%T Zeta Functions and Statistical Mechanics
%J Publications des séminaires de mathématiques et informatique de Rennes
%D 1975
%P 1-10
%N S4
%I Département de Mathématiques et Informatique, Université de Rennes
%U http://archive.numdam.org/item/PSMIR_1975___S4_A22_0/
%G en
%F PSMIR_1975___S4_A22_0

Ruelle, D. Zeta Functions and Statistical Mechanics. Publications des séminaires de mathématiques et informatique de Rennes, no. S4 (1975), article  no. 22, 10 p. http://archive.numdam.org/item/PSMIR_1975___S4_A22_0/

Bibliographie
Cité par

[1] B. Riemann. Uber die Anzahl der Primzahben unterhalb einer gegebenen Grösse. | JFM

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

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

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

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

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

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

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

[20] D. Ruelle. Zeta functions for expanding maps and Anosov flows. To appear. | MR | Zbl