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 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 7 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 »

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