A signal which does not change is trivial to predict: the last observation is a perfect forecast for the next one. Even if the signal changes, this can be a reasonable method of forecasting, and a signal for which this holds is called persistent. A system which changes periodically over time is also easy once you have observed one full cycle. Independent random numbers are easy as well: you do not have to work hard since working hard does not help anyway. The best prediction is just the mean value. Interesting signals are something in between; they are not periodic but they contain some kind of structure which can be exploited to obtain better predictions. (Holger, et.al, 2005)
If stable and unstable manifolds are nonlinear analogs to eigenvectors, then Lyapunov exponents are analogous to eigenvalues in nonlinear systems. Bends and folds in the terrain are the source of the dependence on initial conditions, and the structure of chaotic attractors.