期刊
JOURNAL OF GEOMETRIC MECHANICS
卷 8, 期 2, 页码 169-178出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/jgm.2016002
关键词
Differential system; completely integrable; Poisson bracket; Nambu dynamics; Jacobian multiplier
资金
- Research Agencies of Spain
- Ministerio de Economia y Competitividad [MECD MTM2012-31883, ESP2013-41634-P, ESP-2014-57071-R]
Poisson and integrable systems are orbitally equivalent through the Nambu bracket. Namely, we show that every completely integrable system of differential equations may be expressed into the Poisson-Hamiltonian formalism by means of the Nambu-Hamilton equations of motion and a reparametrisation related by the Jacobian multiplier. The equations of motion provide a natural way for finding the Jacobian multiplier. As a consequence, we partially give an alternative proof of a recent theorem in [13]. We complete this work presenting some features associated to Hamiltonian maximally superintegrable systems.
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