Hyperbolic diffusion in chaotic systems |
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Authors: | P. Borys Z. J. Grzywna J. Łuczka |
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Affiliation: | 1. Department of Physical Chemistry and Technology of Polymers, Section of Physical Chemistry and Biophysics, Silesian University of Technology, 44-100, Gliwice, Poland 2. Institute of Physics, University of Silesia, 40-007, Katowice, Poland
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Abstract: | We consider a deterministic process described by a discrete one-dimensional chaotic map and study its diffusive-like properties. Starting with the corresponding Frobenius-Perron equation we derive an approximate evolution equation for the probability distribution which is a partial differential equation of a hyperbolic type. Consequently, the process is correlated, non-Markovian, non-Gaussian and the information propagates with a finite velocity. This is in clear contrast to conventional diffusion processes described by a standard parabolic diffusion equation with an infinite velocity of information propagation. Our approach allows for a more complete characterisation of diffusion dynamics of deterministic systems. |
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