fractional iterates of arg(z) and |z| JmsNxn Ultimate Fellow Posts: 1,056 Threads: 121 Joined: Dec 2010 03/31/2011, 08:28 PM 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. BenStandeven Junior Fellow Posts: 27 Threads: 3 Joined: Apr 2009 04/04/2011, 04:19 AM (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). JmsNxn Ultimate Fellow Posts: 1,056 Threads: 121 Joined: Dec 2010 04/05/2011, 07:51 PM that was easy « Next Oldest | Next Newest »

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