Symplectic realizations of bihamiltonian structures
نویسنده
چکیده
A smooth manifold M is endowed by a Poisson pair if two linearly independent bivectors c1, c2 are defined on M and moreover cλ = λ1c1+ λ2c2 is a Poisson bivector for any λ = (λ1, λ2) ∈ R 2. A bihamiltonian structure J = {cλ} is the whole 2-dimensional family of bivectors. The structure J (the pair (c1, c2)) is degenerate if rank cλ < dim M,λ ∈ R 2. The degenerate bihamiltonian structures play important role in the theory of completely integrable systems due to the following fact. Let Zcλ denote the set of Casimir functions for cλ and let J0 ⊂ J be the subfamily formed by the Poisson bivectors of maximal rank. It is easy to see that the functions from F0 = SpanR( ⋃
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