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

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.

arXiv comment10 pages, submitted to J. Phys. A:Math. Gen

References in corpus (2)

• Quasi-BiHamiltonian Systems and Separability
• Alternative Structures and Bihamiltonian Systems

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