Superintegrable Systems, Multi-Hamiltonian Structures and Nambu Mechanics in an Arbitrary Dimension
Abstract
A general algebraic condition for the functional independence of 2n-1 constants of motion of an n-dimensional maximal superintegrable Hamiltonian system has been proved for an arbitrary finite n. This makes it possible to construct, in a well-defined generic way, a normalized Nambu bracket which produces the correct Hamiltonian time evolution. Existence and explicit forms of pairwise compatible multi-Hamiltonian structures for any maximal superintegrable system have been established. The Calogero-Moser system, motion of a charged particle in a uniform perpendicular magnetic field and Smorodinsky-Winternitz potentials are considered as illustrative applications and their symmetry algebras as well as their Nambu formulations and alternative Poisson structures are presented.
Cite
@article{arxiv.math-ph/0212070,
title = {Superintegrable Systems, Multi-Hamiltonian Structures and Nambu Mechanics in an Arbitrary Dimension},
author = {A. Tegmen and A. Vercin},
journal= {arXiv preprint arXiv:math-ph/0212070},
year = {2009}
}
Comments
20 pages, 1 table (submitted for publication)