Literature Cited
K. L. Volkovysskii and Ya. G. Sinai, "Ergodic properties of an ideal gas with an infinite number of degrees of freedom," Funkts. Analiz.,5, No. 4, 19–21 (1971).
A. N. Kolmogorov, "A new metric invariant of transitive automorphisms and flows of Lebesgue spaces," Dokl. Akad. Nauk SSSR,119, No. 5, 861–864 (1958).
V. A. Rokhlin, "New progress in the theory of transformations with invariant measure," Uspekhi Mat. Nauk,15, No. 4, 3–26 (1960).
Ya. G. Sinai, "Probabilistic ideas in ergodic theory," Proc. Intern. Math. Congress, Stockholm, 540–559 (1963).
N. N. Bogolyubov, Problems of Dynamical Theory in Statistical Physics, Gostekhizdat, Moscow (1946).
J. Uhlenbeck and J. Ford, Lectures on Statistical Mechanics [Russian translation], Mir, Moscow (1965).
D. W. Jepsen, "Dynamics of a simple many-body system of hard rods," J. Math. Phys.,6, 405–414 (1965).
J. L. Lebowitz, J. K. Percus, and J. Sykes, "Time evolution of the total distribution function of a one-dimensional system of hard rods," Phys. Rev.,171, No. 1, 224–235 (1968).
O. de Pazzis, "Ergodic properties of a semiinfinite hard rods system," Preprint (1971).
V. A. Rokhlin, "Selected problems in the metric theory of dynamical systems," Uspekh. Mat. Nauk,4, No. 2, 57–128 (1949).
F. Spitzer, "Uniform motion with elastic collision of an infinite particle system," J. Math. Mech.,18, No. 10, 973–989 (1969).
T. E. Harris, "Random measures and motions of point processes," Z. Wahrscheindlichkeitstheorie,18, No. 2, 85–115 (1971).
Additional information
Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 6, No. 1, pp. 41–50, January–March, 1972.
Rights and permissions
About this article
Cite this article
Sinai, Y.G. Ergodic properties of a gas of one-dimensional hard rods with an infinite number of degrees of freedom. Funct Anal Its Appl 6, 35–43 (1972). https://doi.org/10.1007/BF01075508
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01075508