S I ] 1 3 O ct 2 00 3 A simple way of making a Hamiltonian system into a bi-Hamiltonian one

@inproceedings{Sergyeyev2003SI,
  title={S I ] 1 3 O ct 2 00 3 A simple way of making a Hamiltonian system into a bi-Hamiltonian one},
  author={Artur Sergyeyev},
  year={2003}
}
Given a Poisson structure (or, equivalently, a Hamiltonian operator) P , we show that its Lie derivative L τ (P) along a vector field τ defines another Poisson structure, which is automatically compatible with P , if and only if [L 2 τ (P), P ] = 0, where [·, ·] is the Schouten bracket. This result yields a new local description for the set of all Poisson structures compatible with a given Poisson structure P such that dim ker P ≤ 1 and leads to a remarkably simple construction of bi… CONTINUE READING

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