Simulation of the chaotic orbit CKI2 with Δt = 0.1 until t = 5000. The left panel shows part of the particle trajectory. The right panel shows the evolution of the relative error in the conserved energy for the RK4 (red line), IMR (blue line), Hamiltonian (green line), and modified Hamiltonian (magenta line) integrators. The RK4 integrator causes the spurious escape of the particle from the orbit. The Hamiltonian scheme, instead, keeps the particle bounded and preserves the energy to machine precision at all times. The IMR and modified Hamiltonian schemes perform equally well in keeping energy errors bounded.