Let $\mathbb{D}=\{|z|<1,\ z\in\mathbb{C}\}$. Are there any other automorphisms in $\mathbb{D}$ except the Blaschke factor $\displaystyle B_{a}(z)=\frac{z-a}{1-\overline{a}z},\ a\in\mathbb{D}$?
I denote with $\overline{a}$ the complex conjugate of $a$.
Thank you for your time,
Chris