Open Access
March 2009 Time transformation and reversibility of Nambu--Poisson systems
J. Gen. Lie Theory Appl. 3(1): 39-52 (March 2009). DOI: 10.4303/jglta/S080103


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.


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Klas MODIN. "Time transformation and reversibility of Nambu--Poisson systems." J. Gen. Lie Theory Appl. 3 (1) 39 - 52, March 2009.


Published: March 2009
First available in Project Euclid: 19 October 2011

zbMATH: 1167.37042
MathSciNet: MR2486609
Digital Object Identifier: 10.4303/jglta/S080103

Primary: 22E70 , 34A26 , 37M99 , 53Z05

Rights: Copyright © 2009 Ashdin Publishing (2009-2013) / OMICS International (2014-2016)

Vol.3 • No. 1 • March 2009
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