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Geometric reduction of Hamiltonian systems

Krzysztof Marciniak·Maciej Blaszak
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Abstract

Given a foliation S of a manifold M, a distribution Z in M transveral to S and a Poisson bivector Πon M we present a geometric method of reducing this operator on the foliation S along the distribution Z. It encompasses the classical ideas of Dirac (Dirac reduction) and more modern theory of J. Marsden and T. Ratiu, but our method leads to formulas that allow for an explicit calculation of the reduced Poisson bracket. Moreover, we analyse the reduction of Hamiltonian systems corresponding to the bivector Π.

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Krzysztof Marciniak, Maciej Blaszak. 2005-03-14. Geometric reduction of Hamiltonian systems. https://doi.org/10.1016/s0034-4877(05)80049-7

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