07/22/2019, 12:24 AM
Just to reiterate my position (har har har), I study dynamics. So when I discuss tetration, it is solely as an example of an iterated function. I could just as easily be discussing pentation or inverse hexation. You want to take one matrix tetrated to a second matrix? Sure. Pentation of quaternions. Yup. A tetration superlog is just a pentation to -1.
My work provides a straight forward algebraic derivation of the entire Classification of Fixed Points including the Abel and Schroeder functional equations and their range. The one limitation of this work is it provides no insight into the Diaphontine irregular neutral fixed points on the Shell-Thron boundary.
Want to hear something cool about the Shell-Thron boundary curve? All systems in physics are measure-preserving dynamical systems. So any physical tetration system will have a base on the Shell-Thron boundary curve. Now strap yourselves in. The complex Shell-Thron boundary curve is associated with multipliers of the roots of unity. Now imagine a multi-dimensional Shell-Thron boundary curve where the multipliers are matrixes, maybe quaternions. The multi-dimensional Shell-Thron boundary is the loci for physically realizable systems.
My work provides a straight forward algebraic derivation of the entire Classification of Fixed Points including the Abel and Schroeder functional equations and their range. The one limitation of this work is it provides no insight into the Diaphontine irregular neutral fixed points on the Shell-Thron boundary.
Want to hear something cool about the Shell-Thron boundary curve? All systems in physics are measure-preserving dynamical systems. So any physical tetration system will have a base on the Shell-Thron boundary curve. Now strap yourselves in. The complex Shell-Thron boundary curve is associated with multipliers of the roots of unity. Now imagine a multi-dimensional Shell-Thron boundary curve where the multipliers are matrixes, maybe quaternions. The multi-dimensional Shell-Thron boundary is the loci for physically realizable systems.
Daniel