Prev: Algorithm for smallest subtree having all of a set of nodes (subtrees)
Next: The FASCINATING Secret Relationship Between PROFLIGATE WHITES and MISLEADER JEWS
From: John on 22 Jun 2010 15:53
What are all mobius transformations that maps the real axis on
itself ?

Thanks
From: Robert Israel on 22 Jun 2010 19:58
John <to1mmy2(a)yahoo.com> writes:

> What are all mobius transformations that maps the real axis on
> itself ?
>
> Thanks

Hint: they must satisfy f(conjugate(z)) = conjugate(f(z)).
--
Robert Israel israel(a)math.MyUniversitysInitials.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
From: spudnik on 22 Jun 2010 20:58
very illuminating.

> They must satisfy f(conjugate(z)) = conjugate(f(z)).


--BP loves Waxman-Obama cap&trade (at least circa Kyoto, or
Waxman's '91 cap&trade on NOX and SO2) --
how about a tiny tax, instead of the Last Bailout
of Wall Street and the "City of London?"
http://larouchepub.com/pr_lar/2010/lar_pac/100621pne_nordyke.html

--le theoreme prochaine du Fermatttt!
http://wlym.com
From: Zdislav V. Kovarik on 23 Jun 2010 11:59


On Tue, 22 Jun 2010, John wrote:

> What are all mobius transformations that maps the real axis on
> itself ?
>
> Thanks
>

Nitpicker's answer: If you mean R, not R(union){infinity}, it's
non-constant linear functions with real coefficients:
w = (z - z0) / (z1 - z0)
where z0, z1 are pre-images of 0 and 1, respectively.

Including infinity: A standard formula is

w = (z - z0) * (z1 - zinfinity) / ((z1 - z0) * (z - zinfinity))

and your condition means that z0, z1, zinfinity are (extended) real.

Exception handling is left to the reader.

Cheers,
ZVK(Slavek).
 | 
Pages: 1
Prev: Algorithm for smallest subtree having all of a set of nodes (subtrees)
Next: The FASCINATING Secret Relationship Between PROFLIGATE WHITES and MISLEADER JEWS