Zeitschrift für Naturforschung A · 1977 · 396 citations · 2 references
Natural SciencesMathematicsPhysicsDynamical SystemsProbability TheoryStochastic ProcessesChaos TheoryDiscrete Dynamical SystemsDiscrete-time Stochastic ProcessesMarkov ProcessesStationary ProcessesStatistical MechanicsChaos In Dynamical SystemsChaotic DynamicsCorrelation DynamicsCorrelation FunctionsNoise Correlation FunctionsOne-dimensional DynamicsStationary Random ProcessesStationary States
Abstract 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.
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