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

作者：Goerlich Andrzej; Kalomenopoulos Marios; Savvidy Konstantin^*; Savvidy George

来源：International Journal of Modern Physics C, 2017, 28(3): 1750032.

DOI：10.1142/S0129183117500322

• Monte-Carlo simulations
• pseudorandom numbers generator
• Ergodic theory
• Anosov hyperbolic systems
• Kolmogorov entropy
• chaos
• periodic trajectories
• MIXMAX generator.

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.

• 出版日期2017-3