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 Iterating at fixed points of b^x bo198214 Administrator Posts: 1,386 Threads: 90 Joined: Aug 2007 09/12/2007, 08:13 PM (This post was last modified: 09/12/2007, 08:19 PM by bo198214.) Daniel Wrote:bo198214 Wrote:I dont know whether I am the first one who realizes that regularly iterating $\exp$ at a complex fixed point yields real coefficients! Moreover they do not depend on the chosen fixed point! I don't think that is true, if I understand you.Yes I withdrawed this assertion (based on an error in my computation) in the preprevious post. However I numerically verified (hopefully this time without error) that the regular iterations at both *real* fixed points coincide for $b. Quote:Just consider the term $\ln(a)^n$ in $\;^{n}b = a + \ln(a)^n \; (1-a) + \ldots$. Öhm, a bit more explanative? Quote:As a side note, consider any two fixed points $a_j,a_k$ for the same $b$, then the fixed point commute under exponentiation ${a_j}^{a_k}= {a_k}^{a_j}$. Yes, this is clear as $a_1^{a_2}=b^{a_1a_2}$ which is independent on the order of $a_1$ and $a_2$. « Next Oldest | Next Newest »

 Messages In This Thread Iterating at fixed points of b^x - by bo198214 - 09/08/2007, 10:02 AM The fixed points of e^x - by bo198214 - 09/08/2007, 10:34 AM The fixed points of b^x - by bo198214 - 09/08/2007, 11:36 AM RE: Iterating at fixed points of b^x - by jaydfox - 09/12/2007, 06:23 AM RE: Iterating at fixed points of b^x - by bo198214 - 09/12/2007, 09:54 AM RE: Iterating at fixed points of b^x - by GFR - 10/03/2007, 11:03 PM RE: Iterating at fixed points of b^x - by Gottfried - 10/04/2007, 06:53 AM RE: Iterating at fixed points of b^x - by bo198214 - 10/04/2007, 01:30 PM RE: Iterating at fixed points of b^x - by bo198214 - 10/04/2007, 05:54 PM RE: Iterating at fixed points of b^x - by Gottfried - 10/04/2007, 11:05 PM RE: Iterating at fixed points of b^x - by GFR - 01/31/2008, 03:07 PM

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