 fractional iterates of arg(z) and |z| - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- Thread: fractional iterates of arg(z) and |z| (/showthread.php?tid=615) fractional iterates of arg(z) and |z| - JmsNxn - 03/31/2011 Is it possible to define a function h(h(z)) = |z|, h(z) =/= |z| or h(h(z)) = arg(z) I wonder because these seem like difficult functions to crack, considering they have no Taylor series. RE: fractional iterates of arg(z) and |z| - BenStandeven - 04/04/2011 (03/31/2011, 08:28 PM)JmsNxn Wrote: Is it possible to define a function h(h(z)) = |z|, h(z) =/= |z| or h(h(z)) = arg(z) I wonder because these seem like difficult functions to crack, considering they have no Taylor series. We could set h(z) = |z| for z with non-negative real part, h(z) = -iz for z with negative real and non-negative imaginary part, and h(z) = iz for z with negative and imaginary parts. Then we'd get h(h(z)) = |z| for all z. A similar technique should work for h(h(z)) = arg(z). RE: fractional iterates of arg(z) and |z| - JmsNxn - 04/05/2011 that was easy