Fractional iteration of x^2+1 at infinity and fractional iteration of exp

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Fractional iteration of x^2+1 at infinity and fractional iteration of exp

mike3

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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.

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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 Catullus - 06/07/2022, 09:05 AM

RE: Fractional iteration of x^2+1 at infinity and fractional iteration of exp - by JmsNxn - 06/08/2022, 12:16 AM

RE: Fractional iteration of x^2+1 at infinity and fractional iteration of exp - by Catullus - 06/08/2022, 01:18 AM

RE: Fractional iteration of x^2+1 at infinity and fractional iteration of exp - by JmsNxn - 06/08/2022, 01:52 AM

RE: Fractional iteration of x^2+1 at infinity and fractional iteration of exp - by Catullus - 06/08/2022, 01:59 AM

RE: Fractional iteration of x^2+1 at infinity and fractional iteration of exp - by JmsNxn - 06/08/2022, 02:06 AM

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

RE: Fractional iteration of x^2+1 at infinity and fractional iteration of exp - by tommy1729 - 06/11/2022, 12:24 PM

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