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On the right we see the tent map increased to this s-value, so one iterate goes to the fixed point of the original tent map. Note this is not the fixed point of the modified (red) tent map.
Now we return s to its original value, and we are very close to the fixed point.
Almost surely, we are not exactly at the fixed point, so because the fixed point is unstable, further iterates will move away from the fixed point.
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| Click either picture to see the consequence of slightly missing the fixed point. |