Geometric reduction of Hamiltonian systems
| Autor: | Krzysztof Marciniak, Maciej Blaszak |
|---|---|
| Rok vydání: | 2005 |
| Předmět: |
Nonlinear Sciences - Exactly Solvable and Integrable Systems
Operator (physics) Dirac (software) FOS: Physical sciences Statistical and Nonlinear Physics Mathematical Physics (math-ph) Foliation Manifold Hamiltonian system Poisson bracket Exactly Solvable and Integrable Systems (nlin.SI) Mathematics::Symplectic Geometry Bivector Mathematical Physics Distribution (differential geometry) Mathematics Mathematical physics |
| Zdroj: | Reports on Mathematical Physics. 55:325-339 |
| ISSN: | 0034-4877 |
| DOI: | 10.1016/s0034-4877(05)80049-7 |
| Popis: | 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. Comment: To appear in Rep. Math. Phys. LaTeX file generated by SWP 4.0 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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