I understand that a set of ODE's can be solved using numerical integration methods e.g. Runge-Kutta
Now, for some Hamiltonian system, we have a set of ODEs specified by Hamilton's equations.
This paper discusses the advantage of a symplectic scheme that conserves the energy of the Hamiltonian system and phase space properties, something which explicit methods like Runge-Kutta do not do.
My question is what is the method for integrating Hamilton's equations in a way that conserves energy, phase-space etc? I cannot seem to find an explicit method laid out anywhere.