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

Авторы: Vivaldi F., Vladimirov I.
Журнал: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Том: 13
Номер: 11
Год издания: 2003
Первая страница: 3373
Последняя страница: 3393
DOI: 10.1142/S0218127403008557
Аннотация: 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.
Добавил в систему: Владимиров Игорь Геннадиевич

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