Integrability of nonlinear dynamical systems and differential geometry structures (Q1332074)

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.