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Degenerate Poisson structures in dimension 3. (English. Russian original) Zbl 0965.53053
Math. Notes 63, No. 4, 509-521 (1998); translation from Mat. Zametki 63, No. 4, 579-592 (1998).
Summary: Formal normal forms of degenerate Poisson structures in dimension 3 are described. The main tool of the study is a spectral sequence previously introduced by the author [Dokl. Math. 54, 706-709 (1996; Zbl 0898.58020), and Math. Notes 61, 180-192 (1997; Zbl 0915.58095)]. In particular, this method allows one to obtain a new proof of the linearizability of Poisson structures with semisimple linear part. However, there are nonlinearizable Poisson structures in dimension 3 as well.
MSC:
53D17 Poisson manifolds; Poisson groupoids and algebroids
37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
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References:
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