Geodesic
Anosov C-systems and random number generators
Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 2, pp. 223-243 Cet article a éte moissonné depuis la source Math-Net.Ru

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We further develop our previous proposal to use hyperbolic Anosov C-systems to generate pseudorandom numbers and to use them for efficient Monte Carlo calculations in high energy particle physics. All trajectories of hyperbolic dynamical systems are exponentially unstable, and C-systems therefore have mixing of all orders, a countable Lebesgue spectrum, and a positive Kolmogorov entropy. These exceptional ergodic properties follow from the C-condition introduced by Anosov. This condition defines a rich class of dynamical systems forming an open set in the space of all dynamical systems. An important property of C-systems is that they have a countable set of everywhere dense periodic trajectories and their density increases exponentially with entropy. Of special interest are the C-systems defined on higher-dimensional tori. Such C-systems are excellent candidates for generating pseudorandom numbers that can be used in Monte Carlo calculations. An efficient algorithm was recently constructed that allows generating long C-system trajectories very rapidly. These trajectories have good statistical properties and can be used for calculations in quantum chromodynamics and in high energy particle physics.
Keywords: Anosov C-system, hyperbolic dynamical system, Kolmogorov entropy, Monte Carlo method, high energy physics, elementary particle, lattice quantum chromodynamics. 
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G. K. Savvidi. Anosov C-systems and random number generators. Teoretičeskaâ i matematičeskaâ fizika, Tome 188 (2016) no. 2, pp. 223-243. http://geodesic.mathdoc.fr/item/TMF_2016_188_2_a1/

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