Stationary solutions of the bogoliubov hierarchy equations in classical statistical mechanics. 2
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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 inRv) 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.
KeywordsNeural Network Generate Function Phase Space Complex System Probability Measure
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- 1.Gurevich, B. M., Suhov, Ju. M.: Commun. math. Phys.49, 63–96 (1976)Google Scholar
- 2.Gallavotti, G., Verboven, E. J.: Nuovo Cimento28B, 274–286 (1975)Google Scholar
- 3.Whittaker, E. T.: A treatise of the analytical dynamics of particles and rigid bodies. Cambridge: University Press 1964Google Scholar
- 4.Siegel, C. L.: Ann. Math.42, 806–822 (1941)Google Scholar
- 5.Siegel, C. L.: Math. Ann.128, 144–170 (1954)Google Scholar
- 6.Bruno, A.: Trudy Mosc. Mathem. Obsch. (in Russian)26, (1972)Google Scholar