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This shadowing result is very strong, because it is special to the
Gauss map. We have shown that * every* computed orbit is
* uniformly* shadowed by a true orbit * for all iterations*,
and that the distance to the true orbit is uniformly bounded by a small
multiple of the machine epsilon ** u**. (Incidentally, I now believe
(1995) that we can replace the 4 in the above with 2, but it's not worth
writing the changes down, really). Most general shadowing results seem to hold only for
finite times, and have bounds more like . Most computational
procedures for * a posteriori* verification of shadowing also fit this
model.
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