Bi-Hamiltonian partially integrable systems

Details Bi-Hamiltonian partially integrable systems Bi-Hamiltonian partially integrable systems

2002-11-29

arxiv.org/abs/math/0211463v4

Mathematics

Dynamical Systems

18 pages

Scientific paper

Given a first order dynamical system possessing a commutative algebra of dynamical symmetries, we show that, under certain conditions, there exists a Poisson structure on an open neighbourhood of its regular (not necessarily compact) invariant manifold which makes this dynamical system into a partially integrable Hamiltonian system. This Poisson structure is by no means unique. Bi-Hamiltonian partially integrable systems are described in some detail. As an outcome, we state the conditions of quasi-periodic stability (the KAM theorem) for partially integrable Hamiltonian systems.

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