Journal of Generalized Lie Theory and Applications

Time transformation and reversibility of Nambu--Poisson systems


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A time transformation technique for Nambu--Poisson systems is developed, and its structural properties are examined. The approach is based on extension of the phase space $\mathscr{P}$ into $\overline{\mathscr{P}}=\mathscr{P}\times\mathbb{R}$, where the additional variable controls the time-stretching rate. It is shown that time transformation of a system on $\mathscr{P}$ can be realised as an extended system on $\overline{\mathscr{P}}$, with an extended Nambu-Poisson structure. In addition, reversible systems are studied in conjunction with the Nambu-Poisson structure. The application in mind is adaptive numerical integration by splitting of Nambu-Poisson Hamiltonians. As an example, a novel integration method for the rigid body problem is presented and analysed.

Article information

J. Gen. Lie Theory Appl., Volume 3, Number 1 (2009), Article ID S080103, 39-52.

First available in Project Euclid: 19 October 2011

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Primary: 37M99: None of the above, but in this section 22E70: Applications of Lie groups to physics; explicit representations [See also 81R05, 81R10] 53Z05: Applications to physics 34A26: Geometric methods in differential equations


MODIN, Klas. Time transformation and reversibility of Nambu--Poisson systems. J. Gen. Lie Theory Appl. 3 (2009), no. 1, Article ID S080103, 39--52. doi:10.4303/jglta/S080103.

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