Real Multivalued/Parametrized Iteration Groups

[tommy1729]

but those iterations probably fail hard on the complex plane ??

that is for complex x and/or s and/or t.


regards

tommy1729

I am not completely sure what you want to see here. A conformal plot of \(S(t+S^{-1}(x))\)?
This is as close to a conformal plot as I can get:

The left image is transformed to the right image by the half iterate of \(-0.5z\).

Im talking About the first 2 pictures you Posted in post nr 1.

You take real iterations of real imput and notice everything works out Nice when considering both
branches .. however when you take real iterations of complex imput , it probably does not work out so well.
Or if you take complex iterations of real imput. Or complex iterations of complex imput.