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Iterating at fixed points of b^x

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Iterating at fixed points of b^x
Daniel Offline
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#10
09/12/2007, 07:50 PM
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. Just consider the term
\( \ln(a)^n \) in \( \;^{n}b = a + \ln(a)^n \; (1-a) + \ldots \).

As a side note, consider any two fixed points \( a_j,a_k \) for the same \( b \), then the fixed point commute under exponentiation \( {a_j}^{a_k}= {a_k}^{a_j} \).
Daniel
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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 GFR - 10/03/2007, 11:03 PM
RE: Iterating at fixed points of b^x - by GFR - 01/31/2008, 03:07 PM

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