symmetry in chaos

Recently SIAM had a deal to get some books from their catalog cheap if you bought the new edition of "Symmetry in Chaos" by Field and Golubitsky. So I did, and couldn't help but try to reproduce some of their figures. I think they might have a typo in their parameters for their figure 2.3 (or I am making some mistake, quite likely), but after exploring a bit with other parameters I got the following, with iterates of