Geometric reduction of Hamiltonian systems

Details Geometric reduction of Hamiltonian systems Geometric reduction of Hamiltonian systems

2005-03-14

arxiv.org/abs/nlin/0503032v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

To appear in Rep. Math. Phys. LaTeX file generated by SWP 4.0

Scientific paper

10.1016/S0034-4877(05)80049-7

Given a foliation S of a manifold M, a distribution Z in M transveral to S and a Poisson bivector \Pi on 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 \Pi.

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