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Bi-Hamiltonian partially integrable systems

G. Giachetta·L. Mangiarotti·G. Sardanashvily
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Abstract

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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G. Giachetta, L. Mangiarotti, G. Sardanashvily. 2003-04-01. Bi-Hamiltonian partially integrable systems. https://doi.org/10.1063/1.1566453

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