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Time transformation and reversibility of Nambu-Poisson systems. (English) Zbl 1167.37042

The author has developed a time transformation technique for Nambu-Poisson systems with the aim to examine their structural properties. The suggested approach is based on the extension of the phase space \(\mathcal{P}\) into \(\mathcal{P}\times \mathbb{R}\), where the additional variable controls the time-stretching rate. The Nambu-Poisson structure is studied in conjunction with reversibility. As application it is shown how to construct fully explicit adaptive numerical integration methods based on splitting of the Nambu-Poisson Hamiltonians, particulary for the free rigid body problem.

MSC:

37M99 Approximation methods and numerical treatment of dynamical systems
22E70 Applications of Lie groups to the sciences; explicit representations
53Z05 Applications of differential geometry to physics
34A26 Geometric methods in ordinary differential equations
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