Let $f:\mathbb{S}^2\to\mathbb{S}^2$ be a continuous north south Transformation, in other words, the point $(0,0,1)$ is a global attractor for $f$ and $(0,0,-1)$ is a global attractor for $f^{-1}$.
How to calculate the entropy of $f$?
I do not want to use the theorem:
$h_{top}(f)=h_{top}(f|NW).$
Thanks in advance!