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arXiv · 1401.1131

A method to generate first integrals from infinitesimal symmetries

Razvan M. Tudoran
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Abstract

We propose a method to construct first integrals of a dynamical system, starting with a given set of independent infinitesimal symmetries. In the case of two infinitesimal symmetries, a rank two Poisson structure on the ambient space it is found, such that the vector field that generates the dynamical system, becomes a Poisson vector field. Moreover, the symplectic leaves and the Casimir functions of the associated Poisson manifold are characterized. Explicit conditions that guarantee Hamilton-Poisson realizations of the dynamical system are also given.

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Razvan M. Tudoran. 2014-03-27. A method to generate first integrals from infinitesimal symmetries. https://doi.org/10.1007/s00009-014-0470-6

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