Theory of Diffusion and Intermittency in Chaotic Systems : Condensed Matter and Statistical Physics

概要

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The statistical-dynamics of A_t obeying A_<t+1> = B(x_t)A_t is investigated, where B is a certain function of x_t generated by a chaotic one-dimensional map x_<t+1> =f(x_t). It is shown that A_t has two complementary aspects, i.e., dlffusion and intermittency, reflecting the log-normal and the non-log-normal characteristics of A_t and governing the low-order statistics of A_t and the higher-order one, respectively. In order to single out the long-time characteristics of the dynamics we introduce the characteristic exponent, which turns out to be important in describing the above two aspects in a clear-cut way. Interrelation between the characteristic exponent and the probability distribution is briefiy discussed. Furthermore, some solvable examples are analyzed as illustrations.
理論物理学刊行会の論文
1984-03-25