The kicked rotator is a prototype model to illustrate the transition from integrability to chaos in Hamiltonian systems and in particular the Kolmogorov–Arnold–Moser theorem. In the limit K = 0 , the system describes the free motion of the rotator, the momentum is conserved (the system is integrable) and the corresponding trajectories are straight lines in the ( θ θ , p ) plane (phase space), that is tori. For small, but non-vanishing perturbation K , instabilities and chaos starts to develop. Only quasi-periodic orbits (represented by invariant tori in phase space) remain stables, while other orbits become unstables. For larger K , invariant tori are eventually destroyed by the perturbation. For the value K = K c ≈ ≈ 0.971635 … … , the last invariant tori connecting θ θ = − − π π and θ θ = π π in phase space is destroyed.