1. A. N. Kolmogorov:Dokl. Akad. Nauk SSSR,98, 527 (1954);V. I. Arnol’d:Sov. Math. Dokl.,2, 247 (1961);3, 136 (1962);J. Moser:Nachr. Akad. Wiss. Göttingen: Math. Phys. Kl. IIa,1, 1 (1962); 87 (1955). The following are reviews on the subject:A. N. Kolmogorov:Proceedings of the 1954 International Congress of Mathematics (Amsterdam, 1957), p. 315; English translation inR. Abraham:Foundations of Mechanics, Appendix D (New York, 1967);V. I. Arnol’d:Russian Math. Surveys,18, 9, 85 (1963);J. Moser:Lectures on Hamiltonian systems, inMemoirs of the American Mathematical Society, No. 81 (Providence, R. I., 1968);V. I. Arnol’d andA. Avez:Problèmes ergodiques de la mécanique classique (Paris, 1967);S. Sternberg:Celestial Mechanics, Chap. 3 (New York, 1969);M. Froeschlé:Annales scientifiques de l’Université de Besançon, Mécanique et physique theorique, III serie, fasc. 8, 3 (1968);R. Barrar:Amer. Journ. Math.,98, 206 (1966);Celestial Mechanics,2, 454 (1970);E. M. McMillan: inTopics in Modern Physics, A tribute toE. U. Condon, edited byW. E. Brittin andH. Odabasi (Boulder, Colo., 1971).
2. Ya. G. Sinai:Sov. Math. Dokl.,4, 1818 (1963); inStatistical Mechanics Foundations and Applications, edited byT. A. Bak (New York, 1967), p. 559;Russian Math. Surveys,25, 137 (1970). For an introduction to both KAM theorem and Sinai’s theorem see:A. S. Wightman:Statistical Mechanics at the Turn of the Decade, edited byE. G. D. Cohen (New York, 1971), p. 1;J. L. Lebowitz: inProceedings of the IUPAP Conference on Statistical Mechanics, Chicago, 1971, to be published;J. Ford: inLectures in Statistical Physics, Vol.2, edited byW. C. Schieve (New York, 1972);J. Ford: submitted toAdv. Chem. Phys.
3. In the article quoted in ref. [2],A. S. Wightman says: « The folklore says that the extension of Sinai’s result to a large class of purely repulsive forces will not be difficult but the inclusion of an attraction will very likely result in a breakdown of ergodicity, at least for some energy surfaces. »
4. V. M. Alexeyev:Actes, Congrès International de Mathematiques, Tome 2 (1970), p. 893.
5. H. Poincaré:Méthodes nouvelles de la mécanique céleste (Paris, 1892);E. Fermi:Zeits. Phys.,24, 261 (1923).