Dubrovin, B. A. 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 Cited in 3 Documents MSC: 37G05 Normal forms for dynamical systems 76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena Keywords:Poisson brackets Citations:Zbl 0591.58012 PDFBibTeX XMLCite \textit{B. A. Dubrovin}, Funct. Anal. Appl. 23, No. 2, 131--133 (1989; Zbl 0711.58027); translation from Funkts. Anal. Prilozh. 23, No. 2, 57--59 (1989) 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.