Consider the dynamical noise called ``pseudonoise'' corrupting a time series generated by a discrete iterated function system (map). Especially, the discrete maps \[ x_{n+1} = f(x_n) \] modified by the two types of maps \[ y_{n+1} = f(y_n) + \eta_n \] or \[ z_{n+1} = f(z_n+\eta_n) \] with noise terms \(\eta_n\) are under consideration. The authors discuss the influence of the dynamical noise \(\eta_n\) on dynamics and the distribution of its ``pseudonoise'' which is determined by the Jacobian of the mapping \(f\). The Gaussian case and quadratic maps are also treated.