Principles of continuation

Abstract

The diagrams in Chapter 2 are idealizations of the results one gets in practice. Numerical reality does not look quite as good as these diagrams. The smooth curves of the bifurcation diagrams are drawn from a skeleton of computed points. It requires—in addition to reliable computational methods— imagination and condence to draw a good diagram from the relatively few points the computer gives us. How to select and construct the points is one concern, and the other is the correct interpretation, which may be summarized by drawing a smooth branch.