# Collective symplectic integrators Artikel i vetenskaplig tidskrift, 2014

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.

## Författare

#### Robert McLachlan

Massey University

#### Klas Modin

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

#### Olivier Verdier

Universitetet i Bergen

#### Nonlinearity

0951-7715 (ISSN)

Vol. 27 6 1525-1542

#### Ämneskategorier

Beräkningsmatematik

Geometri

#### Fundament

Grundläggande vetenskaper

#### DOI

10.1088/0951-7715/27/6/1525

2018-03-27