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# automorphisms of unit disk

All automorphisms of the complex unit disk $\Delta=\{z\in\mathbb{C}:|z|<1\}$ to itself, can be written in the form $f_{a}(z)=e^{{i\theta}}\frac{z-a}{1-\overline{a}z}$ where $a\in\Delta$ and $\theta\in S^{1}$.

This map sends $a$ to $0$, $1/\overline{a}$ to $\infty$ and the unit circle to the unit circle.

Related:

MobiusTransformation, ProofOfConformalMobiusCircleMapTheorem

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Reference

Type of Math Object:

Example

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## Mathematics Subject Classification

30C20*no label found*

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## Recent Activity

Oct 21

new question: Prime numbers out of sequence by Rubens373

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

new question: Prime numbers out of sequence by Rubens373

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

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## Versions

(v6) by brianbirgen 2013-03-22