 99479 D Bosio, F Vivaldi
 Roundoff errors and padic numbers
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Dec 15, 99

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Abstract. We explore some connections between roundoff errors in linear planar
rotations and algebraic number theory. We discretize a map on a lattice
in such a way as to retain invertibility, restricting the system parameter
(the trace) to rational values with powerprime denominator $p^n$.
We show that this system can be embedded into a smooth expansive dynamical
system over the $p$adic integers, consisting of multiplication by a
unit composed with a Bernoulli shift.
In this representation, the original roundoff system corresponds to
restriction to a dense subset of the $p$adic integers.
These constructs are based on symbolic dynamics and on the representation
of the discrete phase space as a ring of integers in a quadratic
number field.
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