- 99-479 D Bosio, F Vivaldi
- Round-off errors and p-adic numbers
Dec 15, 99
(auto. generated ps),
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Abstract. We explore some connections between round-off 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 power-prime 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 round-off 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