  A novel integration method for quadratic vector fields was introduced by
Kahan in 1993. Subsequently, it was shown that Kahan's method preserves a
(modified) measure and energy when applied to quadratic Hamiltonian vector
fields. Here we generalize Kahan's method to cubic resp. higher degree
polynomial vector fields and show that the resulting discretization also
preserves modified versions of the measure and energy when applied to cubic
resp. higher degree polynomial Hamiltonian vector fields.
