2x mod 1 Map
2xmod1Map
Let x_0 be a rational number in the closed interval [0,1], and generate a sequence using the map
| x_(n+1)=2x_n (mod 1). |
(1)
|
Then the number of periodic map orbits of period p (for p prime) is given by
| [画像: N_p=(2^p-2)/p ] |
(2)
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(i.e., the number of period-p repeating bit strings, modulo shifts). Since a typical map orbit visits each point with equal probability, the natural invariant is given by
| rho(x)=1. |
(3)
|
See also
Logistic Map, Tent MapExplore with Wolfram|Alpha
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References
Ott, E. Chaos in Dynamical Systems. Cambridge, England: Cambridge University Press, pp. 26-31, 1993.Referenced on Wolfram|Alpha
2x mod 1 MapCite this as:
Weisstein, Eric W. "2x mod 1 Map." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/2xmod1Map.html