Major references

[JmsNxn]

OMG MphLee, your list is beyond amazing! While I would be happy to have the list on my web site I feel this should probably be managed as a collective resource. Also the list is damn valuable. The best previous list I had seen was Galidakis' list which he inherited from David Renfro. Galidakis had me link to the root of his math site so that folks would be encouraged to look at his research. Having an accessible list like this can improve a site's standing in Google searches.
I need to give this topic significant thought and return to this posting. I'd love to hear other's thoughts.

Do what you like with my list but take it with a grain of salt: I'm not an expert on dynamics. That's just a list I collected during the years of things that seems related and interesting to me.

While for the hyperoperations list, well I'm pretty proud of it... I believe it is almost a complete bibliography on the argument... even if some players are missing... like Nambiar's paper, Galidakis stuff and few other items... But Its all there in my database... but not time to organize the files... 

I will say, of Mphlee's list--it is very foundational. And focuses I'd say 60% on the foundations of hyper-operational "structures". So it's not a list on analytic approaches. I'm not discrediting this--it's just plain to see Mphlee is focused on the categorical nature of hyper-operations.

It is but not categorical. It is actually three lists... the one about hyper-operations, I claim, is pretty much complete. It is all there is around about it imho. The one about Tetration/iterated exp is pretty complete as well, even if some of the oldest papers may be missing it contains almost everything that came out of this forum. No categorical bullshit!

About the list on iteration/dynamics, It is pretty analytic imho. Originally I meant to post it like that, I just added the blue items later, the blue items are about foundational/categorical approach... just for completeness. It is actually two different lists merged.

And the last list is not even an attempt. I know you have the right literature on that topic.

Oh, I apologize Mphlee. The reason I consider your list "not very analytic"--is because there are no analytic papers on these subjects. There really are ZERO hard well developed papers on the hyperoperators, as analytic objects. The closest you'll find is Kouznetsov, who definitely leaves things to be desired (Just because his calculator works, and his intuition/ad hoc reasoning is very correct; doesn't mean it's rigorous).

So, I think I misspoke a tad. What I mean is that there are no good analytic papers on these subjects, and the few you will find, are severely lacking in rigor. Even myself, I only consider 80-90% of my results to be "proven rigorously"--but then, they've never truly been vetted, other than my calculations--which brings us back to Kouznetsov's level of "truth".

I hope you don't think I'm calling these papers categorical, I should've been clearer--I meant these papers look like a good foundation for a categorical approach. Whereby, some of these papers, do not have the quality of rigor, to actually call an analytic solution. But rather, a numerical solution. Where as the good papers, that I identified, are very... not sure the word, "foundational," "about the structure of hyper-operators". Which definitely lead to a "categorical" understanding. I'm aware you're probably the most eminent person on this planet on "Hyper-operators & category theory", because no ones ever touched this before. (No one cares about these subjects, and I love it, because it allows me to work without fear of rediscovering some 100 year old formula no one cares about --doing this, at least it's a new formula... no one cares about).

My main grievance, with saying "it's not a very analytic list"--is, I guess, it's not really a very "RIGOROUS ANALYTIC" list. If anything, a lot of work in tetration/hyper-operation/nested function theory tends to be numerical based. So I would call it more so, numerical analytic. And much of the results end up being effective calculators; but not rigorously proven constructs.

This reminds me of an old joke I heard once. "Of course \(\pi\) is rational, I plugged it in my calculator and out came: \(3.14159265359\)"

So I struggle to call much of hyper-operation/tetration/iteration theory actual analysis. When usually, at best, it is Numerical Analysis. This would definitely fall under Kouznetsov's work. Where the exception is Kouznetsov & Trappman, which is absolutely Analysis in the hard rigorous sense.

Also, don't take too much weight to what I say. I've only had time to post in my free time at night; and I've already started drinking (had too many drinks when I made the comment before), lmao