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Zverev V. V. Фрактальная структура инвариантных распределений Fractal structure of invariant distributions of dissipative random mapsслучайных отображений. Izvestiya VUZ. Applied Nonlinear Dynamics, 1995, vol. 3, iss. 4, pp. 62-72.
Фрактальная структура инвариантных распределений Fractal structure of invariant distributions of dissipative random mapsслучайных отображений
The simple model of a discrete-time dissipative nonlinear dynamical system perturbed by the external fluctuations is studied. It is supposed that the nonlinearity is caused by the intensity-dependent phase rotation of the complex dynamical amplitude. We have shown that the «stationary point» of the equation of motion for a probability distribution (in mixing phase approximation) can be described by the function that is expressed using the fractal set integral. The different determinations of this integrals and the examples of its usage are discussed. We also report some information about the physical systems are described by our simple modei.
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