07/04/2022, 01:28 PM
Yes only a fixpoint at +oo i.
That is a nice idea.
Unfortunately transcendental entire functions are not analytic at complex oo , what was the reason for not talking about it earlier.
anyway , I considered
f(z) = z + exp( 2 * 3.1415926535 i * z )
and plotted f(z),f(f(z)),f(f(f(z))) using Sage
if i can thrust Sage they look like this :
( see pics , where the white bottom is 1 iter , the yellow bottom is 2 iter and the red bottom is 3 iter. further iterates have red bottoms )
One wonders how the half-iterate , 1/3-iterate etc look like.
does it preserve the id(z) + periodic(z) structure ??
I thought I had a book about this , but turns out it was not that.
regards
tommy1729
That is a nice idea.
Unfortunately transcendental entire functions are not analytic at complex oo , what was the reason for not talking about it earlier.
anyway , I considered
f(z) = z + exp( 2 * 3.1415926535 i * z )
and plotted f(z),f(f(z)),f(f(f(z))) using Sage
if i can thrust Sage they look like this :
( see pics , where the white bottom is 1 iter , the yellow bottom is 2 iter and the red bottom is 3 iter. further iterates have red bottoms )
One wonders how the half-iterate , 1/3-iterate etc look like.
does it preserve the id(z) + periodic(z) structure ??
I thought I had a book about this , but turns out it was not that.
regards
tommy1729
