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Differential-geometric Poisson brackets on a lattice. (English. Russian original) Zbl 0711.58027

Funct. Anal. Appl. 23, No. 2, 131-133 (1989); translation from Funkts. Anal. Prilozh. 23, No. 2, 57-59 (1989).
The notion of differential geometric Poisson brackets was introduced by S. P. Novikov and the author in connection with the study of the Poisson brackets of hydrodynamical type and their generalizations [Sov. Math., Dokl. 30, 651-654 (1984); translation from Dokl. Akad. Nauk SSSR 279, No.2, 294-297 (1984; Zbl 0591.58012)]. In the present paper, the author develops a discrete version of such a concept.
Reviewer: I.Kolář

MSC:

37G05 Normal forms for dynamical systems
76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena

Citations:

Zbl 0591.58012
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Full Text: DOI

References:

[1] B. A. Dubrovin and S. P. Novikov, Dokl. Akad. Nauk SSSR,279, No. 2, 294-297 (1984).
[2] B. A. Dubrovin and S. P. Novikov, Dokl. Akad. Nauk SSSR,270, No. 4, 781-785 (1983).
[3] S. P. Novikov, Usp. Mat. Nauk,40, No. 4, 79-89 (1985).
[4] V. G. Drinfel’d, Dokl. Akad. Nauk SSSR,268, No. 2, 285-287 (1983).
[5] M. Adler, Invent. Math.,50, 219-248 (1979). · Zbl 0393.35058
[6] A. G. Élashvili, Trudy Tbilissk. Mat. Inst.,77, 127-137 (1985).
[7] M. Semenov-Tian-Shansky, Publ. RIMS Kyoto Univ.,21, No. 6, 1237-1260 (1985). · Zbl 0674.58038
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