D Bosio and F Vivaldi 2000 Nonlinearity 13 309 doi:10.1088/0951-7715/13/1/315
Round-off errors and p-adic numbers
D Bosio and F Vivaldi
Show affiliationsRecommended by L Bunimovich
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 pn . 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 number field.
- PACS
- MSC
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11Sxx Algebraic number theory: local and p-adic fields
37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
- Subjects
- Dates
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Issue 1 (January 2000)
Received 29 June 1999, in final form 2 November 1999
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Round-off errors and p-adic numbers
D Bosio and F Vivaldi 2000 Nonlinearity 13 309
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-
Evidence for chiral structures in 130Cs
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-
Photoionization of polarized
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-
Cosmological Three-Point Function: Testing the Halo Model against Simulations
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-
Measurement of oscillator strength by tunable laser interferometry
A B Duval and A I McIntosh 1980 J. Phys. D: Appl. Phys. 13 1617
-
A constant temperature hot-wire anemometer
J C Wyngaard and J L Lumley 1967 J. Sci. Instrum. 44 363
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Synthesis and characterization of polyoxometalate nanowires based on a novel microemulsion process
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and 
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Esther Belin-Ferré et al 1996 J. Phys.: Condens. Matter 8 6213
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