Excerpt
A graphical technique for the display of the Lyapunov exponent as a function of control parameters in one-dimensional maps is used to identify coexistence of attractors, superstable curves, highly interleaved basins of attraction in phase space, and highly interleaved regions with different oscillatory modes in parameter space. Furthermore, this technique reveals dramatic' changes of dynamic behavior due to small discontinuities at the maximum of the maps.
Great paper on Lyapunov fractals.