Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 46, Issue 2, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/46/2/025201
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- European Community
- Royal Society of New Zealand
- Australian Research Council
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We show that Kahan's discretization of quadratic vector fields is equivalent to a Runge-Kutta method. When the vector field is Hamiltonian on either a symplectic vector space or a Poisson vector space with constant Poisson structure, the map determined by this discretization has a conserved modified Hamiltonian and an invariant measure, a combination previously unknown amongst Runge-Kutta methods applied to nonlinear vector fields. This produces large classes of integrable rational mappings in two and three dimensions, explaining some of the integrable cases that were previously known.
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