2x mod 1 Map
المؤلف:
Ott, E.
المصدر:
Chaos in Dynamical Systems. Cambridge, England: Cambridge University Press
الجزء والصفحة:
pp. 26-31
4-10-2021
1564
2x mod 1 Map
Let 
be a rational number in the closed interval ![[0,1]](https://mathworld.wolfram.com/images/equations/2xmod1Map/Inline2.gif)
, and generate a sequence using the map
 |
(1)
|
Then the number of periodic map orbits of period 
(for 
prime) is given by
 |
(2)
|
(i.e., the number of period-
repeating bit strings, modulo shifts). Since a typical map orbit visits each point with equal probability, the natural invariant is given by
 |
(3)
|
REFERENCES:
Ott, E. Chaos in Dynamical Systems. Cambridge, England: Cambridge University Press, pp. 26-31, 1993.
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