I found following change of variables that can be also seen as a coordinate system $(y_1, y_2)$ described according to cartesian coordinates $(x_1, x_2)$:

$$y_1 = x_1 · (1+(x_1-1)\sin(\frac{\pi x_2}{2}))$$ $$y_2 = \frac{1}{ 1+(x_1-1)\sin(\frac{\pi x_2}{2})}$$

but do not match any of the common ones (polar, parabolic, hyperbolic, elliptic, bipolar...). I am interested in its name (if exists) in order to search for further info, uses...

  • $\begingroup$ For clarity, is the square applied to the logarithm itself, or is it applied only to $x_i$? $\endgroup$ – Decaf-Math Oct 8 '18 at 19:02
  • $\begingroup$ To whole logarithm, if not could be simplified $\endgroup$ – 24th_moonshine Oct 8 '18 at 19:06

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