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Continued Fractions and Chaos ~~~~~~ Robert M. Corless


Our earlier example of gave a periodic orbit on the HP28S, which has u. The nearby initial point with this orbit under is

As a further curiousity, we note that the machine representation of on the HP28S is an actual fixed point of , allowing us to calculate the exact continued fraction of on a finite machine.

To my knowledge, there are no other examples of initial points which when iterated in floating point give correct results for all time---they all seem to diverge quickly. It would be interesting to prove that the only orbit of which is shadowed by itself is this one.


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