Non-symplectic symmetries and bi-Hamiltonian structures of the rational Harmonic Oscillator
arXiv:hep-th/0210260 · doi:10.1088/0305-4470/35/47/101
Abstract
The existence of bi-Hamiltonian structures for the rational Harmonic Oscillator (non-central harmonic oscillator with rational ratio of frequencies) is analyzed by making use of the geometric theory of symmetries. We prove that these additional structures are a consequence of the existence of dynamical symmetries of non-symplectic (non-canonical) type. The associated recursion operators are also obtained.
10 pages, submitted to J. Phys. A:Math. Gen