Tetration Forum
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

Tongue that was easy