  It is a classical theorem of Liouville that Hamiltonian systems preserve
volume in phase space. Any symplectic Runge-Kutta method will respect this
property for such systems, but it has been shown that no B-Series method can be
volume preserving for all volume preserving vector fields (BIT 47 (2007)
351-378 and IMA J. Numer. Anal. 27 (2007) 381-405). In this paper we show that
despite this result, symplectic Runge-Kutta methods can be volume preserving
for a much larger class of vector fields than Hamiltonian systems, and discuss
how some Runge-Kutta methods can preserve a modified measure exactly.
