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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

Major Section:

Reference

Type of Math Object:

Example

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## Mathematics Subject Classification

30C20*no label found*

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## Recent Activity

Apr 22

new question: Prove that for any sets A, B, and C, An(BUC)=(AnB)U(AnC) by St_Louis

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new image: information-theoretic-distributed-measurement-dds.png by rspuzio

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new collection: On the Information-Theoretic Structure of Distributed Measurements by rspuzio

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new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia

new question: Prove that for any sets A, B, and C, An(BUC)=(AnB)U(AnC) by St_Louis

Apr 20

new image: information-theoretic-distributed-measurement-dds.png by rspuzio

new image: information-theoretic-distributed-measurement-4.2 by rspuzio

new image: information-theoretic-distributed-measurement-4.1 by rspuzio

new image: information-theoretic-distributed-measurement-3.2 by rspuzio

new image: information-theoretic-distributed-measurement-3.1 by rspuzio

new image: information-theoretic-distributed-measurement-2.1 by rspuzio

Apr 19

new collection: On the Information-Theoretic Structure of Distributed Measurements by rspuzio

Apr 15

new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia

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## Versions

(v6) by brianbirgen 2013-03-22