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Collective symplectic integrators
Institute of Fundamental Sciences, Massey University, Palmerston North, New Zealand.
Department of Mathematical Sciences, Chalmers University of Technology, Gothenburg, Sweden.
Department of Mathematics, University of Bergen, Norway.ORCID iD: 0000-0003-3699-6244
2014 (English)In: Nonlinearity, ISSN 0951-7715, E-ISSN 1361-6544, Vol. 27, no 6, 1525-1542 p.Article in journal (Refereed) Published
Abstract [en]

We construct symplectic integrators for Lie-Poisson systems. The integrators are standard symplectic (partitioned) Runge-Kutta methods. Their phase space is a symplectic vector space equipped with a Hamiltonian action with momentum map J whose range is the target Lie-Poisson manifold, and their Hamiltonian is collective, that is, it is the target Hamiltonian pulled back by J. The method yields, for example, a symplectic midpoint rule expressed in 4 variables for arbitrary Hamiltonians on so(3)*. The method specializes in the case that a sufficiently large symmetry group acts on the fibres of J, and generalizes to the case that the vector space carries a bifoliation. Examples involving many classical groups are presented.

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2014. Vol. 27, no 6, 1525-1542 p.
Keyword [en]
symplectic integrators, Lie-Poisson systems, reduction
National Category
Computational Mathematics
URN: urn:nbn:se:umu:diva-89403DOI: 10.1088/0951-7715/27/6/1525ISI: 000337159700020OAI: diva2:720446
Available from: 2014-05-29 Created: 2014-05-29 Last updated: 2014-07-18Bibliographically approved

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Verdier, Olivier
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