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.
This talk has not been recorded due to unpublished work