26. (a) The second return map (light line), together with the first return map (dark line) for s = 2. |
(b) The 2-cycle is shown by the dashed square. |
(c) From the dashed square, we see one point, x, of the 2-cycle is less than 1/2, while the other, y, is greater than 1/2. Then using equation (2) |
x_{n+1} = s*x_{n} if x_{n} <= 0.5 |
x_{n+1} = s*(1 - x_{n}) if x_{n} > 0.5 |
we see y = s*x and x = s*(1 - y). Combining these,
x = |
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