Invariant Distributions and Stationary Correlation Functions of One-Dimensional Discrete Processes

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The connection between one-dimensional dynamical laws generating discrete processes and their invariant densities as well as their stationary correlaton functions is discussed. In particular the changes occuring under a special equivalence transformation are considered. Correlation functions are used to describe the gradual transition from periodic states to chaotic states via periodic motions with superimposed nonlinearity noise.