Geometric reduction of Hamiltonian systems
Exactly Solvable and Integrable Systems
2009-11-11 v1 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.nlin/0503032,
title = {Geometric reduction of Hamiltonian systems},
author = {Krzysztof Marciniak and Maciej Blaszak},
journal= {arXiv preprint arXiv:nlin/0503032},
year = {2009}
}
Comments
To appear in Rep. Math. Phys. LaTeX file generated by SWP 4.0