  The hyperbolic Anosov C-systems have a countable set of everywhere dense
periodic trajectories which have been recently used to generate pseudorandom
numbers. The asymptotic distribution of periodic trajectories of C-systems with
periods less than a given number is well known, but a deviation of this
distribution from its asymptotic behaviour is less known. Using fast
algorithms, we are studying the exact distribution of periodic trajectories and
their deviation from asymptotic behaviour for hyperbolic C-systems which are
defined on high dimensional tori and are used for Monte-Carlo simulations. A
particular C-system which we consider in this article is the one which was
implemented in the MIXMAX generator of pseudorandom numbers. The generator has
the best combination of speed, reasonable size of the state, and availability
for implementing the parallelization and is currently available generator in
the ROOT and CLHEP software packages at CERN.
