4
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Now, suppose the transformation(in 2d) I am working with has two
separate functions for $x$ and $y$.

That is, the transformation for $x$ is of the form $$ x'=\frac{x}{x+y} $$ and the transformation of $y$ is $$ y'=\frac{y}{x+y} $$ Each is an LFT (The schwarzian derivatives are $0$) but is
the transform as a whole still considered an LFT?

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    If you treat $(x,y)$ as a complex variable $z=x+iy$, then $\frac{z}{\Re z+\Im z}$ is no longer a linear fractional transformation.2010-11-17
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    But suppose, in my original post, that x and y are strictly positive reals in the typical 2d x/y plane?2010-11-18
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    Only component-wise, but remember that two-dimensional geometric transformations can be shown to be equivalent to certain operations on complex numbers. So for the transformation as a whole, I don't think so, due to what I mentioned in my first comment. (I would be happy to be proven wrong.)2010-11-18
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    I think I understand, mostly. 2d is just an example though. I was hoping to examine some properties of this under higher dimensions. For example in 3d: x'=x/(x+y+z),y'=y/(x+y+z),z'=z/(x+y+z). Where x,y,z are all positive reals(I am, for other reasons, only concerned with the positive orthant).2010-11-18

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