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Fractal structure and Gaussian distribution in chaotic Brownian motion

✍ Scribed by Toshihiro Shimizu

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
604 KB
Volume
196
Category
Article
ISSN
0378-4371

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✦ Synopsis

In Brownian motion driven by a chaotic sequence of iterates of a map F(y), x(t)= -yx(t) + f(t), where f(t) = y, +~/v~ for m-< t _-< (n + 1)z (n = 1, 2 .... ) and y, +, = F(y,), the fractal structure and the z-dependence of the recurrence relation (x,+l, x,), where x, = x (t = nr), are studied. The recurrence relation is shown to change from a shape similar to F(y) into a diagonal strip, which does not depend on the details of F(y), if ~" is decreased.

Consequently it is shown that the stationary distribution of x, changes from a similar shape as the invariant density of F(y) into a Gaussian shape.

πŸ“œ SIMILAR VOLUMES

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✍ Toshihiro Shimizu πŸ“‚ Article πŸ“… 1990 πŸ› Elsevier Science 🌐 English βš– 796 KB

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