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 Fractional iteration of x^2+1 at infinity and fractional iteration of exp mike3 Long Time Fellow Posts: 368 Threads: 44 Joined: Sep 2009 06/08/2011, 09:31 PM (This post was last modified: 06/08/2011, 10:06 PM by mike3.) (06/08/2011, 09:55 AM)bo198214 Wrote: Again similar to the Schröder case, we have an alternative expression: $g^t(x)=\lim_{n\to\infty} g^{-n}\left(g^n(x)^{2^t}\right)$ If we even roll back our conjugation with $1/x$ we get: $f^t(x)=\lim_{n\to\infty} f^{-n}\left(f^n(x)^{2^t}\right)$. Numerically this also looks very convincing: Something seems really wrong. These limit formulas are giving me what appears to be abs(x), regardless of the value of t I use. « Next Oldest | Next Newest »

 Messages In This Thread Fractional iteration of x^2+1 at infinity and fractional iteration of exp - by bo198214 - 06/08/2011, 09:55 AM RE: Fractional iteration of x^2+1 at infinity and fractional iteration of exp - by Gottfried - 06/08/2011, 01:09 PM RE: Fractional iteration of x^2+1 at infinity and fractional iteration of exp - by tommy1729 - 06/08/2011, 01:18 PM RE: Fractional iteration of x^2+1 at infinity and fractional iteration of exp - by bo198214 - 06/08/2011, 07:59 PM RE: Fractional iteration of x^2+1 at infinity and fractional iteration of exp - by JmsNxn - 06/08/2011, 07:26 PM RE: Fractional iteration of x^2+1 at infinity and fractional iteration of exp - by mike3 - 06/08/2011, 09:31 PM RE: Fractional iteration of x^2+1 at infinity and fractional iteration of exp - by bo198214 - 06/08/2011, 09:48 PM RE: Fractional iteration of x^2+1 at infinity and fractional iteration of exp - by mike3 - 06/08/2011, 10:08 PM RE: Fractional iteration of x^2+1 at infinity and fractional iteration of exp - by bo198214 - 06/08/2011, 10:12 PM RE: Fractional iteration of x^2+1 at infinity and fractional iteration of exp - by mike3 - 06/08/2011, 10:58 PM RE: Fractional iteration of x^2+1 at infinity and fractional iteration of exp - by bo198214 - 06/09/2011, 05:56 AM

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