Mokhov, O. I. Local third-order Poisson brackets. (English. Russian original) Zbl 0604.58029 Russ. Math. Surv. 40, No. 5, 233-234 (1985); translation from Usp. Mat. Nauk 40, No. 5(245), 257-258 (1985). Special contact transformations are introduced preserving the translation invariance of Hamiltonian operators. A theorem is announced without proof about the classification of third order translation invariant Hamiltonian operators based on these special contact transformations. Reviewer: M.Farkas Cited in 6 Documents MSC: 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems 58E30 Variational principles in infinite-dimensional spaces Keywords:contact transformations; translation invariance; Hamiltonian operators; classification of third order translation invariant Hamiltonian operators PDFBibTeX XMLCite \textit{O. I. Mokhov}, Russ. Math. Surv. 40, No. 5, 233--234 (1985; Zbl 0604.58029); translation from Usp. Mat. Nauk 40, No. 5(245), 257--258 (1985) Full Text: DOI