Ergodic maps with Lyapunov exponent equal to zero

Some properties of the ergodic maps defined on the finite and infinite intervals, that are characterized by the exact invariant densities and the Lyapunov exponent /spl lambda/, equal to zero, are studied. The solution of the spectral problem for the Perron-Frobenius operators, corresponding to such maps is found. It is shown that the invariant distributions are the indifferent motionless points of these operators. The examples of conjugated maps with /spl lambda/=0, including the rational generator of pseudorandom values distributed by Cauchy law, are constructed.