Some recent results on the Kahan-Hirota-Kimura discretization
Seminar Room 1, Newton Institute
We show that Kahan's discretization of quadratic vector fields is equivalent to a Runge-
Kutta method. In case the vector field is Hamiltonian, with constant Poisson structure, the
map determined by this discretization preserves a (modified) integral and a (modified) invariant measure. This produces large classes of integrable rational mappings, explaining some of the integrable cases that were previously known, as well as yielding many new ones.