Classical invariant manifolds are invariant sets in the phase space  of an autonomous dynamical system. In contrast,
LCSs are only required to be invariant in the extended phase space. This means that even if the underlying dynamical system is autonomous, the LCSs of the system over the interval  will generally be time-dependent, acting as the evolving skeletons of observed coherent trajectory patterns. Figure 2b shows the difference between an attracting LCS and a classic unstable manifold of a saddle point, for evolving times, in an autonomous dynamical system.