4.8  Projects

Exercise 4.9.  Secondary islands
In figure 4.3 (section 4.1) we see a chain of six secondary islands in the oscillation region. Carry out the Poincaré-Birkhoff construction to obtain the alternating sequence of stable and unstable fixed points for this island chain.

Exercise 4.10.  Invariant curves of the standard map

a.  Make programs that reproduce figures 4.22 and 4.23. You will need to develop an effective method of estimating the probability of visitation. There is one suggestion of how to do that in the text, but you may find a better way.

b.  As the parameter K is increased beyond the critical value, the golden invariant curve ceases to exist. Investigate how the method for finding invariant curves fails beyond the critical value of K.