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Thread: Möbius transformation conformal

  1. #1
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    Möbius transformation conformal

    I would like to understand how to choose the right Mobius transformation. For example, the Möbius transformation that maps upper half-plane onto the unit disk is:

    z --> (z-i)/(z+i)

    The Möbius transformation that maps the unit disk one to one onto the right half-plane is:

    z--> (1+z)/(1-z)

    I would like to understand how one gets to this Möbius transformations. Thank you!
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  2. #2
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    Re: Möbius transformation conformal

    I'm not really sure what you're asking but maybe have a look at this
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  3. #3
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    Re: Möbius transformation conformal

    Choose three distinct points on the boundary of the upper half plane
    move from left to right

    e.g. $\{0,1,\infty \}$

    choose three distinct points on the unit circle
    moving counterclockwise

    e.g. $\{-1,-i,1\}$

    find a transformation that maps $\displaystyle 0 $ to $\displaystyle -1$, $\displaystyle 1 $ to $\displaystyle -i$, and $\displaystyle \infty$ to $\displaystyle 1$
    Thanks from topsquark
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