Abstract
In the preceding paper under the same title we have formulated a theorem which describes the set of states (i.e., probability measures on phase space of an infinite system of particles inR v) corresponding to stationary solutions of the BBGKY hierarchy. We have proved the following statement: ifG is a Gibbs measure (Gibbs random point field) corresponding to a stationary solution of the BBGKY hierarchy, then its generating function satisfies a differential equation which is “conjugated” to the BBGKY hierarchy. The present paper deals with the investigation of the “conjugated” equation for the generating function in particular cases.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Gurevich, B. M., Suhov, Ju. M.: Commun. math. Phys.49, 63–96 (1976)
Gallavotti, G., Verboven, E. J.: Nuovo Cimento28B, 274–286 (1975)
Whittaker, E. T.: A treatise of the analytical dynamics of particles and rigid bodies. Cambridge: University Press 1964
Siegel, C. L.: Ann. Math.42, 806–822 (1941)
Siegel, C. L.: Math. Ann.128, 144–170 (1954)
Bruno, A.: Trudy Mosc. Mathem. Obsch. (in Russian)26, (1972)
Author information
Authors and Affiliations
Additional information
Communicated by J. L. Lebowitz
Rights and permissions
About this article
Cite this article
Gurevich, B.M., Suhov, I.M. Stationary solutions of the bogoliubov hierarchy equations in classical statistical mechanics. 2. Commun.Math. Phys. 54, 81–96 (1977). https://doi.org/10.1007/BF01609838
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01609838