Suppose we have the tent map, $T_\mu(x) = \mu \min(x, 1-x)$ with parameter $\mu = 2$ (so it is topologically conjugate to the logistic map with parameter $4$).
For any point $x_0 \in [0, 1] \cap \mathbb{Q}$, does there exist an equation/algorithm I can use to quickly compute $T_2^k(x_0)$ for any $k$ (especially when $k$ is very large)? In the question linked here, where I ask the same question for the logistic map, the answer is "yes, there does exist such a method."
However, because the tent-map is peicewise non-smooth and cannot be approximated well with any polynomial of relatively low degree (since we need to accurately simulate the steps of the map, which are sensitive to initial conditions), my thinking is that the answer in this case would be "no, there does not exist such a method", but I am unable to prove this. Does anyone have a proof or argument otherwise?