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 Solving tetration for base 0 < b < e^-e bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 09/12/2009, 08:35 AM (This post was last modified: 09/12/2009, 08:40 AM by bo198214.) (09/12/2009, 08:07 AM)mike3 Wrote: Hmm. However in the emails, you mentioned the use of a "multiplier" that works similar to the derivative at the fixed point but for a cycle. Generally the multiplier of a cycle $p_1,\dots,p_n$ (i.e. $p_{k+1}=f(p_k)$ and $f(p_n)=p_1$) is defined as: $f'(p_1)\cdot f'(p_2)\dots f'(p_n)$. This is equal to the multiplier of $f^{\circ n}$ at any point of the cycle (by the chain rule). Example n=2 $f(f(x))'=f'(f(x))\cdot f'(x)$. If you now plug in $x=p_1$ you get $f'(p_2)\cdot f'(p_1)$ and if you plug in $x=p_2$ you get the same result $f'(p_1)\cdot f'(p_2)$. If you would depict the tangents at the left and right fixed point in the graph before, they would be parallel. But this approach to consider $f^{\circ 2}$ already failed. « Next Oldest | Next Newest »

 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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