Non-symplectic symmetries and bi-Hamiltonian structures of the rational Harmonic Oscillator

摘要

The existence of bi-Hamiltonian structures for the rational HarmonicOscillator (non-central harmonic oscillator with rational ratio of frequencies)is analyzed by making use of the geometric theory of symmetries. We prove thatthese additional structures are a consequence of the existence of dynamicalsymmetries of non-symplectic (non-canonical) type. The associated recursionoperators are also obtained.