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Re: Mobius (Linear Fractional) transformation, need some help.
Posted:
Feb 19, 2006 9:57 AM
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graumet wrote:
> I am pretty stumped here. I am trying to work problem 4 p.80 in
> Ahlfors' 'complex analysis'. The problem:
>
> show that any four points can be carried by a linear [fractional?]
> transformation to positions 1,-1,k,-k where the value of k depends on
> the points. how many solutions are there, and how are they related.
>
> I would cry is someone posted a solution, but would be very thankfull
> for some hints
I think a transformation of this kind preserves the cross-ratio.
So you could start by computing the cross-ration of {1,-1,k,-k}.
--
Timothy Murphy
e-mail (<80k only): tim /at/ birdsnest.maths.tcd.ie
tel: +353-86-2336090, +353-1-2842366
s-mail: School of Mathematics, Trinity College, Dublin 2, Ireland
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