  The uniformly hyperbolic Anosov C-systems defined on a torus have very strong
instability of their trajectories, as strong as it can be in principle. These
systems have exponential instability of all their trajectories and as such have
mixing of all orders, nonzero Kolmogorov entropy and a countable set of
everywhere dense periodic trajectories. In this paper we are studying the
properties of their spectrum and of the entropy. For a two-parameter family of
C-system operators A(N,s), parametrised by the integers N and s, we found the
universal limiting form of the spectrum, the dependence of entropy on N and the
period of its trajectories on a rational sublattice. One can deduce from this
result that the entropy and the periods are sharply increasing with N. We
present a new three-parameter family of C-operators A(N,s,m) and analyse the
dependence of its spectrum and of the entropy on the parameter m. We developed
our earlier suggestion to use these tuneable Anosov C-systems for multipurpos
Monte-Carlo simulations. The MIXMAX family of random number generators based on
Anosov C-systems provide high quality statistical properties, thanks to their
large entropy, have the best combination of speed, reasonable size of the
state, tuneable parameters and availability for implementing the
parallelisation.
