{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T14:27:21Z","timestamp":1772288841359,"version":"3.50.1"},"reference-count":27,"publisher":"World Scientific Pub Co Pte Lt","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2003,11]]},"abstract":"<jats:p> We analyze the sequences of round-off errors of the orbits of a discretized planar rotation, from a probabilistic angle. It was shown [Bosio &amp; 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. <\/jats:p>","DOI":"10.1142\/s0218127403008557","type":"journal-article","created":{"date-parts":[[2003,12,18]],"date-time":"2003-12-18T09:02:05Z","timestamp":1071738125000},"page":"3373-3393","source":"Crossref","is-referenced-by-count":17,"title":["PSEUDO-RANDOMNESS OF ROUND-OFF ERRORS IN DISCRETIZED LINEAR MAPS ON THE PLANE"],"prefix":"10.1142","volume":"13","author":[{"given":"FRANCO","family":"VIVALDI","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"IGOR","family":"VLADIMIROV","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS, UK"},{"name":"Mathematics Department, University of Queensland, Brisbane QLD 4072, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02575441"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(93)90920-U"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(94)90191-0"},{"key":"rf4","volume-title":"Set-Valued Analysis","author":"Aubin J.-P.","year":"1990"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(87)90100-X"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1023\/A:1002067315057"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(94)00103-0"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/13\/1\/315"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(98)00319-4"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127498001133"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/s00332-001-0450-4"},{"key":"rf14","volume-title":"A Second Course in Number Theory","author":"Cohn H.","year":"1962"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-22278-2"},{"key":"rf16","volume-title":"Martingale Limit Theory and Its Application","author":"Hall H.","year":"1980"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-2789(96)00243-6"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4754(96)00063-8"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1063\/1.166240"},{"key":"rf21","first-page":"1321","volume":"5","author":"Lowenstein J. 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