Dust in the Tent

Recall the highest point of the tent map has height s/2. Consequently, if s > 2 the top of the tent map extends above the top of the unit square. Graphical iteration implies the points near 1/2 iterate out of the unit square, and then on to -infinity (top figure). Then points that iterate to the middle will escape to -infinity (bottom picture).

Continuing, the points that do not escape to -infinity form a Cantor set. Can you find the dimension of this Cantor set as a function of s?

On the Cantor set, the tent map is chaotic.

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