• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Is successor function analytic? Daniel Fellow Posts: 200 Threads: 65 Joined: Aug 2007 09/22/2022, 12:19 PM Consider the Ackermann successor function $$\varphi(u)$$ such that $$\varphi(a \uparrow ^m b)=a \uparrow ^{m+1} b$$. Is $$\varphi(u)$$ analytic? If so then the complex dynamics of $$\varphi^n(u)$$ can be studied where there is a finite real fixed at  point $$a\uparrow^\infty\infty$$. For example where $$1 \leq a < e^\frac{1}{e}$$. Daniel bo198214 Administrator Posts: 1,594 Threads: 101 Joined: Aug 2007 6 hours ago (09/22/2022, 12:19 PM)Daniel Wrote: Consider the Ackermann successor function $$\varphi(u)$$ such that $$\varphi(a \uparrow ^m b)=a \uparrow ^{m+1} b$$.  Is this well-defined? I mean to define it that way you would need something like:  if $$a_1\uparrow^m b_1=a_2\uparrow^m b_2$$ then $$a_1=a_2$$ and $$b_1=b_2$$ ? « Next Oldest | Next Newest »

 Possibly Related Threads… Thread Author Replies Views Last Post The bounded analytic semiHyper-operators JmsNxn 4 7,982 06/29/2022, 11:46 PM Last Post: JmsNxn Bounded Analytic Hyper operators JmsNxn 25 44,368 04/01/2015, 06:09 PM Last Post: MphLee Proof Ackermann function extended to reals cannot be commutative/associative JmsNxn 1 5,778 06/15/2013, 08:02 PM Last Post: MphLee generalizing the problem of fractional analytic Ackermann functions JmsNxn 17 40,447 11/24/2011, 01:18 AM Last Post: JmsNxn Proof Ackermann function cannot have an analytic identity function JmsNxn 0 4,050 11/11/2011, 02:26 AM Last Post: JmsNxn extension of the Ackermann function to operators less than addition JmsNxn 2 7,520 11/06/2011, 08:06 PM Last Post: JmsNxn Ackermann function and hyper operations andydude 3 11,417 04/18/2011, 05:08 PM Last Post: bo198214 A specific value of the Ackermann function tetrator 12 23,490 11/02/2008, 02:47 PM Last Post: Finitist

Users browsing this thread: 1 Guest(s)