Results 1 to 2 of 2

Math Help - Mobius transformation

  1. #1
    Member
    Joined
    Sep 2008
    Posts
    166

    Mobius transformation

    I am trying to find the most general Mobius transformation that maps the right half-plane to the unit disc carrying the point 5 to the origin. I find a particular Mobius transformation is \frac{z-5}{z+5}. But how do I find the most general one?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by dori1123 View Post
    I am trying to find the most general Mobius transformation that maps the right half-plane to the unit disc carrying the point 5 to the origin. I find a particular Mobius transformation is \frac{z-5}{z+5}. But how do I find the most general one?
    You compose that transformation with a Möbius transformation of the unit disc that fixes the origin. But the only such transformations are rotations about the origin. So the most general transformation will be \lambda\frac{z-5}{z+5}, where \lambda is any complex number of absolute value 1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Mobius Transformation
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: November 27th 2011, 05:58 AM
  2. Mobius Transformation
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: November 16th 2011, 06:16 AM
  3. mobius transformation
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 2nd 2010, 06:44 AM
  4. Mobius transformation
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: October 27th 2009, 07:39 AM
  5. Mobius transformation
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: October 25th 2009, 07:33 PM

Search Tags


/mathhelpforum @mathhelpforum