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Distribution of periodic trajectories of C-K systems MIXMAX pseudorandom number generator

Andrzej Görlich

The Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark

E-mail Address: goerlich@nbi.dk

Current address: Institute of Physics, Jagiellonian University, Lojasiewicza 11, PL 30-348 Krakow, Poland.

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Marios Kalomenopoulos

Institute of Nuclear and Particle Physics, Demokritos National Research Center, Ag. Paraskevi, GR15342, Athens, Greece

E-mail Address: klerade@gmail.com

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Konstantin Savvidy

Institute of Nuclear and Particle Physics, Demokritos National Research Center, Ag. Paraskevi, GR15342, Athens, Greece

E-mail Address: k.savvidis@cern.ch

Corresponding author.

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George Savvidy

Institute of Nuclear and Particle Physics, Demokritos National Research Center, Ag. Paraskevi, GR15342, Athens, Greece

E-mail Address: savvidy@inp.demokritos.gr

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https://doi.org/10.1142/S0129183117500322Cited by:3 (Source: Crossref)

Abstract

We are considering the hyperbolic C-K systems of Anosov–Kolmogorov which are defined on high dimensional tori and are used to generate pseudorandom numbers for Monte-Carlo simulations. All trajectories of the C-K systems are exponentially unstable and pseudorandom numbers are represented in terms of coordinates of very long chaotic trajectories. The C-K systems on a torus have countable set of everywhere dense periodic trajectories and their distribution play a crucial role in coding and implementation of the pseudorandom number generator. The asymptotic distribution of chaotic trajectories of C-K systems with periods less than a given number is well known in mathematical literature, but a deviation from its asymptotic behavior is unknown. Using analytical and computer calculations, we are studying a distribution function of periodic trajectories and their deviation from asymptotic behavior. The corresponding MIXMAX generator has the best combination of speed, size of the state and is currently available generator.

Keywords:

PACS Nos.: 11.25.Hf, 123.1K

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