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arXiv · hep-th/0210260

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

José F. Cariñena·Giuseppe Marmo·Manuel F. Rañada
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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.

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José F. Cariñena, Giuseppe Marmo, Manuel F. Rañada. 2002-10-28. Non-symplectic symmetries and bi-Hamiltonian structures of the rational Harmonic Oscillator. https://doi.org/10.1088/0305-4470%2F35%2F47%2F101

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