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, 10:08 PM (This post was last modified: 06/08/2011, 10:09 PM by mike3.)

(06/08/2011, 09:48 PM)bo198214 Wrote:
(06/08/2011, 09:31 PM)mike3 Wrote: Something seems really wrong. These limit formulas are giving me what appears to be abs(x), regardless of the value of t I use.
Regardless of the value of t you use??? It looks the same for all t?
Could you reproduce my picture for t=1/2?

Nope. Setting t = 1/2 and using

\( f(x) = x^2 + 1 \)
\( f^{-1}(x) = \sqrt{x - 1} \)

then taking your formula for \( f^{-n}(f^n(x) \sqrt{2}) \) yields what appears to be \( |x| \) as \( n \rightarrow \infty \). The g formula doesn't work either.

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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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