Rank-Wise Approximations of Hyper-Operations

[JmsNxn]

I'm doubtful it'd be possible though, it'd be really cool if it was. The trouble is every tetration induces an iteration, and as I remarked that iterations \(f^{\circ s}(z)\) can't be holomorphic in the neighborhood of two fixed points.

What if the different Schröder iterations flowed together nicely?

That would be quite the function!

I'm doubtful it'd be possible though, it'd be really cool if it was. The trouble is every tetration induces an iteration, and as I remarked that iterations \(f^{\circ s}(z)\) can't be holomorphic in the neighborhood of two fixed points.

The only way I can interpret "flowed together nicely" is Kneser. Kneser makes sure \(L\) and it's complex conjugate \(L^*\) flow together properly. Though, they are never allowed to produce an iteration holomorphic in the neighborhood of both points.

And I mean this absolutely, you can't have holomorphy in \(s\) on some domain, and holomorphy in \(z\) on some domain which includes \(L,L^*\)--the closest you get is Kneser.