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.
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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.
![[Annotate]](/organics/icons/sannotate.gif){kind=icon}
![[Shownotes]](../gif/annotate/shide-141.gif)