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

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

2002-10-28

arxiv.org/abs/hep-th/0210260v1

J.Phys. A35 (2002) L679-L686

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, submitted to J. Phys. A:Math. Gen

Scientific paper

10.1088/0305-4470/35/47/101

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.

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