>Remember, Li and Yorke's "Period Three Implies Chaos" results, like those >of Feigenbaum, only apply to unimodal maps of the interval.
Don't these occur far more often (in non-contrived physical situations) that any other maps? (Clearly, a subjective question.)
>The "Feigenbaum >constant" is not the same for all systems,
Right. It is 4.6692 . . . only for the unimodal, finite second derivative maps that seem to occur most often. It is -2.8336 . . . for the Fibonacci cascade of the zero-slope cubic nonlinearity, for example.
>and there are maps and ODEs that >period triple from simple behavior. In fact, just a couple of weeks ago, one >of my students found a period tripling sequence in a physical parametrically >driven pendulum.
I would love to learn more about this. Was this period tripling sequence (presumably meaning a trifurcation cascade) discovered by accident, or was the pendulum specifically rigged to produce it?