automorphisms of unit disk

All automorphisms of the complex unit diskMathworldPlanetmath Δ={z:|z|<1} to itself, can be written in the form fa(z)=eiθz-a1-a¯z where aΔ and θS1.

This map sends a to 0, 1/a¯ to and the unit circle to the unit circle.

Title automorphisms of unit disk
Canonical name AutomorphismsOfUnitDisk
Date of creation 2013-03-22 13:36:48
Last modified on 2013-03-22 13:36:48
Owner brianbirgen (2180)
Last modified by brianbirgen (2180)
Numerical id 6
Author brianbirgen (2180)
Entry type Example
Classification msc 30C20
Related topic MobiusTransformation
Related topic ProofOfConformalMobiusCircleMapTheorem