Modern ergodic theory

Physics Today

Volumn 26, Issue 2, 1973, Pages 23-29

  Lebowitz, Joel L ^a   Penrose, Oliver ^b  

^a YESHIVA UNIVERSITY   (United States)

^b OPEN UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84953658545     PISSN: 00319228     EISSN: 19450699     Source Type: Trade Journal    
DOI: 10.1063/1.3127948     Document Type: Article

References (31)

1. 1.V. I. Arnold, A. Avez, Ergodic Problems of Statistical Mechanics, Benjamin, New York (1968);
2. J. Ford, “The Transition from Analytic Dynamics to Statistical Mechanics,” to be published in Advances in Chemical Physics, 1972
3. J. L. Lebowitz, “Hamiltonian Flows and Rigorous Results in Non-equilibrium Statistical Mechanics,” in Proceedings of the IUPAP Conference on Statistical Mechanics, University of Chicago Press (1972);
4. O. Lanford, “Ergodic Theory and Approach to Equilibrium for Finite and Infinite Systems,” to be published in Proceedings of the 100th Anniversary of the Boltzmann Equation, Vienna, 1972;
5. Ya. G. Sinai, “Ergodic Theory,” to be published in Proceedings of the 100th Anniversary of the Boltzmann Equation;
6. A. S. Wightman, in Statistical Mechanics at the Turn of the Decade (E. G. D. Cohen, ed.) Marcel Dekker, New York (1971).
7. Y. G. Sinai, Sov. Math.-Dokl. 4, 1818 (1963);
8. “Ergodicity of Boltzmann's Equations” in Statistical Mechanics, Foundations and Applications (T. A. Bak, ed.) Benjamin, New York (1967);
9. Russian Mathematical Reviews 25, 137 (1970).
10. 3.G. H. Walker, J. Ford, Phys. Rev. 188, 416 (1969).
11. 4.O. Penrose, Foundations of Statistical Mechanics, Pergamon, Oxford (1970) chapter III.
12. 5.D. ter Haar, Elements of Statistical Mechanics, Holt, Rinehart and Winston, New York (1964), Appendix 1, paragraph 5;
13. O. Penrose, Foundations of Statistical Mechanics, Pergamon, Oxford (1970), page 40;
14. S. G. Brush, Transport Theory and Statistical Physics 1(4), 287 (1971).
15. 6.V. I. Arnold, A. Avez, ref. 1, page 16.
16. 7.A. N. Kolmogorov, “Address to the 1954 International Congress of Mathematicians,” [translated in R. Abrahams, Foundations of Mechanics, Benjamin, New York (1967), Appendix D].
17. 8.Enrico Fermi: Collected Papers, Volume II, University of Chicago Press, Chicago (1965) page 978.
18. 9.G. H. Lunsford, J. Ford, J. Math. Phys. 13, 700 (1972).
19. 10.M. Hénon, C. Heiles, Astron. J. 69, 73 (1964).
20. 11.V. I. Arnold, A. Avez, ref. 1, page 25.
21. 12.J. von Neumann, Annals of Math. 33, 587 (1932).
22. 13.E. Hopf, J. Math. and Phys. 13, 51 (1934);
23. Ergoden Theone, Springer, Berlin (1937).
24. 14.J. W. Gibbs, Elementary Principles in Statistical Mechanics, Dover, New York (1960) page 144.
25. 15.H. Poincaré, Acta Math. 13, 1 (1890);
26. Oeuvres 7, 262;
27. J. W. Gibbs, reference 14, page 139.
28. 16.T. Erber, B. Schweizer, A. Sklar, to be published in Comm. Math. Phys.
29. 17.D. Ornstein, B. Weiss, to be published in Israel J. Mathematics.
30. 18.P. R. Halmos, Lectures on Ergodic Theory, Mathematical Soc. of Japan () page 9;
31. V. I. Arnold, A. Avez, reference 1, page 8.