06/01/2021, 09:37 PM
Not so sure about what it would have to do with tetration, but this seems related to periodic points of polynomial maps. I don't have a strong familiarity with Elliptic curves, but it seems we're encoding the periodic points of a polynomial (in complex dynamics), with the group structure of Elliptic curves, and points with finite torsion. Further, this seems much closer to "using complex dynamics to solve problems in elliptic curves" rather than "using elliptic curves to solve problems in complex dynamics." Interesting read though.
As to adopting more mainstream mathematics; I think this is something which has to happen naturally. Mathematicians are slow to adopt new methods. I mean, no one's even translated Kneser's paper from 1950s; and there only exists scattered interest in the problem. But additionally, the solution of these problems is so specialized (for each solution); that it would take some grand unifying thing before people even cared. Until someone relates tetration to something like, fluid dynamics or the Riemann Hypothesis; unfortunately, no one will care. I, however, think this is a good thing. As over saturation of a field means you're constantly competing to beat other people to the chase. I prefer the small little vacuum of research around tetration.
Honestly, what tetration really needs is attention from someone like John Conway (who unfortunately passed last year)--whose whole schtick was this nonsense mathematics that no one ever thought would have any use. I think iteration theory is something we're just beginning to see become mainstream. And by the time it is, people will look at work that was done amongst those here, and say to themselves "well, I guess they beat us to the chase." Kouznetsov's textbook, for instance, is what we should be working towards; collaborating and collating all the work in a packaged one size serves all. I truly believe that Kouznetsov's regular iteration is the first step towards a "black-box" mechanism in iteration theory.
Regards, James
As to adopting more mainstream mathematics; I think this is something which has to happen naturally. Mathematicians are slow to adopt new methods. I mean, no one's even translated Kneser's paper from 1950s; and there only exists scattered interest in the problem. But additionally, the solution of these problems is so specialized (for each solution); that it would take some grand unifying thing before people even cared. Until someone relates tetration to something like, fluid dynamics or the Riemann Hypothesis; unfortunately, no one will care. I, however, think this is a good thing. As over saturation of a field means you're constantly competing to beat other people to the chase. I prefer the small little vacuum of research around tetration.
Honestly, what tetration really needs is attention from someone like John Conway (who unfortunately passed last year)--whose whole schtick was this nonsense mathematics that no one ever thought would have any use. I think iteration theory is something we're just beginning to see become mainstream. And by the time it is, people will look at work that was done amongst those here, and say to themselves "well, I guess they beat us to the chase." Kouznetsov's textbook, for instance, is what we should be working towards; collaborating and collating all the work in a packaged one size serves all. I truly believe that Kouznetsov's regular iteration is the first step towards a "black-box" mechanism in iteration theory.
Regards, James
