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Integrability of nonlinear dynamical systems and differential geometry structures. (English. Russian original) Zbl 0808.58027

Ukr. Math. J. 45, No. 3, 448-456 (1993); translation from Ukr. Mat. Zh. 45, No. 3, 419-427 (1993).
Some aspects of the application of differential geometry methods to the study of the integrability of a nonlinear dynamical system \(u_ t = K[u]\), where \(K : M \to T(M)\) is a vector field on \(M = C^ \infty (N,M)\), \(N\), \(M\) are smooth finite-dimensional real manifolds. The author restricts himself to a class of vector fields on \(M\), which possess additional differential geometry structures such as the Hamiltonian property and the Noetherian invariance. The paper is interesting and well written.
Reviewer: A.Klíč (Praha)

MSC:

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.)
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
58A20 Jets in global analysis
58D15 Manifolds of mappings
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