This is interesting because:
- Regular regions of phase space in Hamiltonian systems contain manifolds.
- Particles can only move along the manifolds.
- In 'good' symplectic integrators the manifold structure of the system is preserved.
- Although it is perturbed.
- the solution to the integration has many of the characteristics
of the true solution.
- Included energy conservation!
- is exactly conserved.
- Oscillates around real value because is not H.