Pseudo-randomness of round-off errors in discretized linear maps on the plane

Vivaldi, FRANCO and Vladimirov, Igor (2003) Pseudo-randomness of round-off errors in discretized linear maps on the plane. International Journal of Bifurcation And Chaos, 13 11: 3373-3393. doi:10.1142/S0218127403008557

Author Vivaldi, FRANCO
Vladimirov, Igor
Title Pseudo-randomness of round-off errors in discretized linear maps on the plane
Journal name International Journal of Bifurcation And Chaos   Check publisher's open access policy
ISSN 0218-1274
Publication date 2003-11
Sub-type Article (original research)
DOI 10.1142/S0218127403008557
Volume 13
Issue 11
Start page 3373
End page 3393
Total pages 21
Editor L.O. Chua
Place of publication Singapore
Publisher World Scientific Publishing Co. Pte. Ltd.
Collection year 2003
Language eng
Subject C1
780101 Mathematical sciences
230199 Mathematics not elsewhere classified
Abstract We analyze the sequences of round-off errors of the orbits of a discretized planar rotation, from a probabilistic angle. It was shown [Bosio & Vivaldi, 2000] that for a dense set of parameters, the discretized map can be embedded into an expanding p-adic dynamical system, which serves as a source of deterministic randomness. For each parameter value, these systems can generate infinitely many distinct pseudo-random sequences over a finite alphabet, whose average period is conjectured to grow exponentially with the bit-length of the initial condition (the seed). We study some properties of these symbolic sequences, deriving a central limit theorem for the deviations between round-off and exact orbits, and obtain bounds concerning repetitions of words. We also explore some asymptotic problems computationally, verifying, among other things, that the occurrence of words of a given length is consistent with that of an abstract Bernoulli sequence.
Keyword Mathematics, Interdisciplinary Applications
Multidisciplinary Sciences
Round-off Errors
Pseudo-random Sequences
P-adic Dynamics
Q-Index Code C1

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
2004 Higher Education Research Data Collection
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Citation counts: TR Web of Science Citation Count  Cited 13 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 15 times in Scopus Article | Citations
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Created: Wed, 15 Aug 2007, 01:55:54 EST