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Normal forms of Poisson structures in three-dimensional space. (English. Russian original) Zbl 0877.58023
Russ. Math. Surv. 51, No. 4, 741-742 (1996); translation from Usp. Mat. Nauk 51, No. 4, 163-164 (1996).
The paper provides a formal classification of degenerate Poisson structures in three-dimensional space \(\mathbb{R}^3\). The proofs are based on the calculation of the spectral sequence constructed in the author’s preprint [‘Schouten brackets and Lie-Sklyanin algebras’, Preprint ISBN 82-553-0962-4, No. 18, Univ. Oslo: Inst. Math., 1-28 (1995)].
MSC:
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
37G05 Normal forms for dynamical systems
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