Pentation fractal

[bo198214]

Regular iteration at a single fixed point is absolutely holomorphic..? I'm confused. What was the problem, is that if we perform regular iteration about \(z \approx L\) the fixed point, then it won't be real valued on the real line, but it's still holomorphic. Also, if you perform the regular iteration on the real line, as Kouznetsov refers to it, you get the crescent iteration, which is again holomorphic. The absolute power of regular iteration is that it's always holomorphic.

Perhaps you got confused by what I wrote, using \(\theta\) mappings you can perturb the regular iteration, but then it is no longer holomorphic in a neighborhood hood of the fixed point, is that what you meant to say?

Now I am confused