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According to this Wikipedia article, Möbius transformations are known by many different names, including:

homographies, homographic transformations, linear fractional transformations, bilinear transformations, and fractional linear transformations.

Is there a preferred name which is most commonly used?

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Thanks for the markdown correction. – bryanj Jun 15 '13 at 18:17
"M\"obius", "homographic" and "fractional linear" are all used very often. I would certainly not call myself these transformations "bilinear" (I haven't even understood the question was about M\"obius transformations before opening it). – Start wearing purple Jun 15 '13 at 18:19
In my experience, "Möbius" and "fractional linear" are the most commonly used names. – Andreas Blass Jun 15 '13 at 18:31
Thanks a bunch. "Möbius" and "fractional linear" are in both collections, so looks like they may be the way to go. – bryanj Jun 15 '13 at 19:12

To not leave the question without an answer: it transpired in comments that "Möbius transformation" and "fractional linear transformation" are the most commonly used terms.

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