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Feb 19, 2017 at 12:41 comment added მამუკა ჯიბლაძე Conjugating, one can reduce to the cases $\varphi_k(x,y):=(e^{\frac{2\pi i}n}x,e^{\frac{2\pi i k}n}y)$. It should not be difficult to compute all possible cases, I think they form (up to invertible changes of variables) a finite-dimensional vector space for each $n$.
Feb 19, 2017 at 12:34 history edited Alan Muniz CC BY-SA 3.0
Improved question
Feb 18, 2017 at 8:20 comment added მამუკა ჯიბლაძე Say, $f(x,y)=\frac{1-x}{1-y}=(1-x)(1+y+y^2+...)$, with $\varphi(x,y)=(y,x)$?
Feb 17, 2017 at 23:40 history asked Alan Muniz CC BY-SA 3.0