Geometric reduction of Hamiltonian systems
Marciniak, Krzysztof ; Blaszak, Maciej
arXiv, 0503032 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-03-14
Classification:  Nonlinear Sciences - Exactly Solvable and Integrable Systems,  Mathematical Physics 
@article{0503032,
     author = {Marciniak, Krzysztof and Blaszak, Maciej},
     title = {Geometric reduction of Hamiltonian systems},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0503032}
}

Marciniak, Krzysztof; Blaszak, Maciej. Geometric reduction of Hamiltonian systems. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0503032/