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# Collective symplectic integrators

Robert McLachlan ; Klas Modin (Institutionen för matematiska vetenskaper, matematik) ; Olivier Verdier
Nonlinearity (0951-7715). Vol. 27 (2014), 6, p. 1525-1542.

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 \$\mathfrak{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.

CPL Pubid: 198992

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Institutionen för matematiska vetenskaper, matematik (2005-2016)