12/14/2022, 05:56 AM
https://math.eretrandre.org/publications.html
This is a list of Trappmann's work.
I suggest linking to Ecalle, and Milnor, and Baker's work too; as their work is very foundational to much of the tools. I can give a meagre list if asked.
I suggest Paulsen & Cowgill for Kneser, as I feel it is a slightly stronger paper on the construction of Kneser than Kouznetsov http://myweb.astate.edu/wpaulsen/tetration2.pdf. Also, it is much more a direct translation of Kneser's work, with some caveats. As there is no english translation of Kneser, this can be frustrating. Also, the Paulsen approach is very much Kneser's approach--where as Kouznetsov uses his own method.
For Sheldon Levenstein (sheldonison), I suggest linking to the megathread on fatou.gp.
For Andy, I do believe there is a similar megathread, where Andy's method is properly described. Which actually dates back to Peter Walker. Walker's construction is pretty brief, and he has priority--it was a bit of an aside in his work, but Andy really crunched the numbers.
Despite my participation on this forum, I don't feel I've really done enough work in tetration to warrant "major references"--though the fractional calculus approach seems like it could fit; as it directly relates these things to analytic number theory. And relates iterations of functions to mellin transforms; which is pretty cool, if I do say so myself
I know mphlee, who's much more organized than me, has a list of major publications in the scope of tetration. He could be more help here, lol.
This is a list of Trappmann's work.
I suggest linking to Ecalle, and Milnor, and Baker's work too; as their work is very foundational to much of the tools. I can give a meagre list if asked.
I suggest Paulsen & Cowgill for Kneser, as I feel it is a slightly stronger paper on the construction of Kneser than Kouznetsov http://myweb.astate.edu/wpaulsen/tetration2.pdf. Also, it is much more a direct translation of Kneser's work, with some caveats. As there is no english translation of Kneser, this can be frustrating. Also, the Paulsen approach is very much Kneser's approach--where as Kouznetsov uses his own method.
For Sheldon Levenstein (sheldonison), I suggest linking to the megathread on fatou.gp.
For Andy, I do believe there is a similar megathread, where Andy's method is properly described. Which actually dates back to Peter Walker. Walker's construction is pretty brief, and he has priority--it was a bit of an aside in his work, but Andy really crunched the numbers.
Despite my participation on this forum, I don't feel I've really done enough work in tetration to warrant "major references"--though the fractional calculus approach seems like it could fit; as it directly relates these things to analytic number theory. And relates iterations of functions to mellin transforms; which is pretty cool, if I do say so myself
I know mphlee, who's much more organized than me, has a list of major publications in the scope of tetration. He could be more help here, lol.