# automorphisms of unit disk

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

This map sends $a$ to $0$, $1/\overline{a}$ to $\mathrm{\infty}$ 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 |