Zeta Functions and Statistical Mechanics

D. Ruelle

Publications mathématiques et informatique de Rennes (1975)

  • Issue: S4, page 1-10

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Ruelle, D.. "Zeta Functions and Statistical Mechanics." Publications mathématiques et informatique de Rennes (1975): 1-10. <http://eudml.org/doc/274886>.

@article{Ruelle1975,
author = {Ruelle, D.},
journal = {Publications mathématiques et informatique de Rennes},
language = {eng},
number = {S4},
pages = {1-10},
publisher = {Département de Mathématiques et Informatique, Université de Rennes},
title = {Zeta Functions and Statistical Mechanics},
url = {http://eudml.org/doc/274886},
year = {1975},
}

TY - JOUR
AU - Ruelle, D.
TI - Zeta Functions and Statistical Mechanics
JO - Publications mathématiques et informatique de Rennes
PY - 1975
PB - Département de Mathématiques et Informatique, Université de Rennes
IS - S4
SP - 1
EP - 10
LA - eng
UR - http://eudml.org/doc/274886
ER -

References

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  1. [1] B. Riemann. Uber die Anzahl der Primzahben unterhalb einer gegebenen Grösse. JFM26.0215.03
  2. [2] A. Weil. Numbers of solutions of equations in finite fields. Bull. Am. Math. Soc.55, (1949), 497-508 Zbl0032.39402MR29393
  3. [3] P. Deligne. La conjecture de Weil I. IHES Publ. math.43, (1974), 273-307 Zbl0287.14001MR340258
  4. [4] M. Artin and B. Mazev. On periodic points. Ann. of Math.81, (1965), 82-99 Zbl0127.13401MR176482
  5. [5] S. Smale. Differentiable dynamical systems. Bull. A.M.S.73, (1967), 747-817 Zbl0202.55202MR228014
  6. [6] A. SelbergHarmonic analysis and discontinuous groups in weakly symmetric Riemann spaces with applications to Dirichlet series. J. Indian Math. Soc.20, (1956), 47-87 Zbl0072.08201MR88511
  7. [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) Zbl0048.43401MR53029
  8. [8] Ch. Newman. Classifying general Ising models. Lecture given at the International Colloquium on Mathematical Methods in Quantum Field Theory. Marseille, June 1975 MR479247
  9. [9] J. Guckenheimer. Axiom A + no cycles ζ f ( t ) rational. Bull. A.M.S.76, (1970), 592-594 Zbl0196.27002MR254871
  10. [10] A. Manning. Axiom A diffeomorphisms have rational zeta functions. Bull. London Math. Soc.3, (1971), 215-220 Zbl0219.58007MR288786
  11. [11] M. Atiyah and R. Bott. Notes on the Lefshetz fixed point theorem for elliptic complexes. Harvard University. Fall 1964 Zbl0161.43101
  12. [12] R. Bowen. Markov partitions for Axiom A diffeomorphisms. Amer. J. Math.92, (1970), 725-747 Zbl0208.25901MR277003
  13. R. Bowen. Markov partitions and minimal sets for Axiom A diffeomorphisms. Amer. J. Math .92, (1970), 907-918. Zbl0212.29104MR277002
  14. [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. Zbl0182.55003MR233038
  15. 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 Zbl0194.22602MR250352
  16. [14] R. Bowen and O.E. Lanford III. Zeta functions of restrictions of the shift map. Proc. Symp. pure math.14, (1970),43-49 Zbl0211.56501
  17. [15] Ia. G. Sinai. Gibbsian measures in ergodic theory. Uspekhi mat. Nauk27 n° 4, (1972), 21-64. English translation Russian math. Surveys166, (1972), 21-69. Zbl0255.28016MR399421
  18. [16] D. Ruelle. Generalized zeta-functions for Axiom A basic sets. To appear Zbl0316.58016MR400311
  19. [17] P. Walters. A variational principle for the pressure of continuous transformations. Amer. J. Math. To appear Zbl0318.28007MR390180
  20. [18] R. Bowen. Symbolic dynamics for hyperbolic flows. Amer. J. Math.95, (1973),429-460 Zbl0282.58009MR339281
  21. [19] A. Grothendieck. Produits tensoriels topologiques et espaces nucléaires. Mémoirs of the Amer. math. Soc.16, Providence, R.I., (1955) Zbl0064.35501MR75539
  22. A. Grothendieck. La théorie de Fredholm. Bull. Soc. math.France, 84, (1956), 319-384. Zbl0073.10101MR88665
  23. [20] D. Ruelle. Zeta functions for expanding maps and Anosov flows. To appear. Zbl0329.58014MR420720

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