Let $I=[0,1]$ and $\alpha \in ( 0,1)$. Define the Tent map, $T: I \rightarrow I$ by
$T(x)= x/\alpha$ for $x \in [0,\alpha]$ and $(1-x)/(1-\alpha)$ for $x \in [\alpha,1]$
Find the measure theoretic entropy.
For the case $\alpha =1/2$, I can calculate the Entropy. However, for the general case I am not sure how to do it. Since as soon as I start calculating $T^{-i}P$ for a given partition $P$ the expressions become very complicated.
I am guessing that I should move to a representation in terms of shift dynamics but I am not sure how. Could anybody give me a hint?