One Dimensional Maps - Equations

Quadratic or Logistic Map

F(x) = ax(1-x)

Sine Map

F(x) = ¼a sin(x)

Tent Map

F(x) = ax x<½
F(x) = a(1-x) x>½

Power Law

F(x) = (½)1+b - |x-½|1+b

Circle Map

:
F(x) = x + b - (a/2) sin(2 x) mod 1

Shift Map

F(x) = ax mod 1
i.e.
F(x) = ax x<1/a;
F(x) = a(x-1/a) x>1/a;
The value a=2 is usually used giving the Bernoulli shift map.

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Last modified Thursday, January 6, 2000
Michael Cross