  The behavior of a family of dissipative dynamical systems representing
transformations of two-dimensional torus is studied on a discrete lattice and
compared with that of conservative hyperbolic automorphisms of the torus.
Applying dissipative dynamical systems to generation of pseudorandom numbers is
shown to be advantageous and equidistribution of probabilities for the
sequences of bits can be achieved. A new algorithm for generating uniform
pseudorandom numbers is proposed. The theory of the generator, which includes
proofs of periodic properties and of statistical independence of bits at
distances up to logarithm of mesh size, is presented. Extensive statistical
testing using available test packages demonstrates excellent results, while the
speed of the generator is comparable to other modern generators.
