Chaos is impossible for linear systems with separable Hamiltonians.

As discussed in Section 1.2.2, linear systems always obey the principle of linear superposition. This implies that the Hamiltonians for such systems are always separable. A separable Hamiltonian can always be transformed into a sum of separate Hamiltonians with one element in the sum corresponding to each subsystem. In effect, a separable system is one where the interactions among subsystems can be transformed away leaving the subsystems independent of each other. The whole is the sum of the par