  There is a growing interest in the conservation of invariants when
numerically solving a system of ordinary differential equations. Methods that
exactly preserve these quantities in time are known as geometric integrators.
In this paper we apply the recently developed mimetic framework to the solution
of a system of first order ordinary differential equations. Depending on the
discrete Hodge-* employed, two classes of arbitrary order time integrators are
derived. It is shown that the one based on a canonical Hodge-* results in a
symplectic integrator, whereas the one based on a Galerkin Hodge-* results in
an energy preserving integrator. A set of numerical tests confirms these
theoretical results.
