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Classification of Poisson structures. (English. Russian original) Zbl 0898.58020
Dokl. Math. 54, No. 2, 706-709 (1996); translation from Dokl. Akad. Nauk Nauk, Ross. Akad. Nauk 350, No. 3, 304-307 (1996).
From the text: “In this work, Poisson structures that vanish at some point are classified. To find the normal forms of such Poisson structures, we apply the method of spectral sequences. The spectral sequences that we use are spectral sequences of Poisson cohomologies. Using a \(\mu\)-adic filtration in a Poisson complex, we find the normal forms of Poisson structures and formulate the conditions of their sufficiency”.

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
37G05 Normal forms for dynamical systems
37A30 Ergodic theorems, spectral theory, Markov operators