Geodesic
Potential of Gibbs measure corresponding to steady solution of the BBGKY hierarchy for nonfinite interaction
Teoretičeskaâ i matematičeskaâ fizika, Tome 69 (1986) no. 2, pp. 259-272

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For a non-negative interaction and Gibbs measure with non-negative finiteparticle potential, the problem of the connection between steady solutions and first integrals is solved. 
@article{TMF_1986_69_2_a9,
     author = {I. Yu. Musina},
     title = {Potential of {Gibbs} measure corresponding to steady solution of the {BBGKY} hierarchy for nonfinite interaction},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {259--272},
     publisher = {mathdoc},
     volume = {69},
     number = {2},
     year = {1986},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1986_69_2_a9/}
}
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I. Yu. Musina. Potential of Gibbs measure corresponding to steady solution of the BBGKY hierarchy for nonfinite interaction. Teoretičeskaâ i matematičeskaâ fizika, Tome 69 (1986) no. 2, pp. 259-272. http://geodesic.mathdoc.fr/item/TMF_1986_69_2_a9/