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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)

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.)

Citations:

Zbl 0712.58032
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