$$g(x)=\begin{cases} 2x & \text{if } x \in [0,1/2] \\ 2(1-x) & \text{if } x \in (1/2,1] \end{cases}$$
Could you please help me to find out how many different orbits of length $n$ are possible under iteration by $g$.
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Why don't you just count them? – user10354138 Oct 27 '23 at 13:43
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What have you tried? Have you tried computing them for some $n$'s? – Keen-ameteur Oct 27 '23 at 14:23