Geometric reduction of Hamiltonian systems
arXiv:nlin/0503032 · doi:10.1016/S0034-4877(05)80049-7
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.
To appear in Rep. Math. Phys. LaTeX file generated by SWP 4.0
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