Novikov, S. P.; Mal’tsev, A. Ya. The Liouville form of averaged Poisson brackets. (English. Russian original) Zbl 0807.58016 Russ. Math. Surv. 48, No. 1, 155-157 (1993); translation from Usp. Mat. Nauk. 48, No. 1(289), 155-156 (1993). This paper contains the discussion and a correction of several results from the paper by B. A. Dubrovin and the first author [Russ. Math. Surv. 44, No. 6, 35-124 (1989); translation from Usp. Mat. Nauk 44, No. 6(270), 29-98 (1989; Zbl 0712.58032)]. Especially, the principle of conservation of Hamiltonian structure under averaging is corrected and the statement of Theorem 1 in §6 is discussed. Reviewer: A.Klíč (Praha) Cited in 1 Document MSC: 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) Keywords:Poisson bracket of hydrodynamic type; averaging method; involutory integral Citations:Zbl 0712.58032 PDFBibTeX XMLCite \textit{S. P. Novikov} and \textit{A. Ya. Mal'tsev}, Russ. Math. Surv. 48, No. 1, 155--156 (1993; Zbl 0807.58016); translation from Usp. Mat. Nauk. 48, No. 1(289), 155--156 (1993) Full Text: DOI