Hyperbolic Rotation

Also known as the Lorentz Transformation or Procrustian Stretch. Leaves each branch of the Hyperbola $x'y'=xy$ invariant and transforms Circles into Ellipses with the same Area.

$$\begin{eqnarray*} x'&=&\mu^{-1} x\\ y'&=&\mu y. \end{eqnarray*}$$