Solving tetration for base 0 < b

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Solving tetration for base 0 < b < e^-e

bo198214 Offline

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09/12/2009, 07:20 AM

(09/12/2009, 06:56 AM)bo198214 Wrote: So I would consider the regular iteration of \( g(x)=f^{\circ 2}(x)=b^{b^x} \) and then just always take the half of the iteration number \( f^{\circ t}(x)=g^{\circ t/2}(x) \).

The interesting thing is that \( g \) not only has the two attracting fixed points \( p_1 \) and \( p_2 \) but also a repelling fixed point in between. Which is attractive for \( g^{-1} \) in the range \( (p_1,p_2) \).

Graph for b=0.01 with p1=0.941482102273016 and p2=0.0130925205079953.

So why not do regular iteration at that inbetween fixed point?

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Messages In This Thread

Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 02:00 AM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 06:56 AM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 07:20 AM

RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 07:40 AM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 07:47 AM

RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 08:07 AM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 08:35 AM

RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 08:50 AM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/12/2009, 03:48 PM

RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/12/2009, 09:04 PM

RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 06:14 AM

RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/13/2009, 07:24 AM

RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 09:57 AM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/13/2009, 11:23 AM

RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 11:44 AM

RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/14/2009, 09:43 PM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/17/2009, 08:01 AM

RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/17/2009, 11:03 AM

RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 01:34 PM

RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/13/2009, 07:34 PM

RE: Solving tetration for base 0 < b < e^-e - by Gottfried - 09/14/2009, 02:02 PM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/13/2009, 08:08 AM

RE: Solving tetration for base 0 < b < e^-e - by mike3 - 09/13/2009, 09:49 AM

RE: Solving tetration for base 0 < b < e^-e - by tommy1729 - 09/18/2009, 12:16 PM

RE: Solving tetration for base 0 < b < e^-e - by bo198214 - 09/18/2009, 01:00 PM

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