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    Biholomorphisms of the disc

    T-2XFTY

    The unit-disc biholomorphisms are precisely rotations composed with Blaschke factors.Suggest a slogan

    The group of biholomorphisms of the unit disc \(\DD\) onto itself is \[ \Aut(\DD)=\ts{z\mapsto e^{i\theta}\,\frac{\alpha-z}{1-\bar\alpha z}\st\theta\in\RR,\ \alpha\in\DD}, \] the rotations composed with the Blaschke factors \(\psi_\alpha\).