File:PowIteT.jpg
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Summary
| Title / Description
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Explicit plot of th Iteration of the quadratic function, id est, power function for power 2; for various values of number of iteration. Here, : $\!\!\!\!\!\!\!\!\!\!\ (1) ~ ~ ~ T(z)=\mathrm{Pow}_2(z)=z^2=\exp\Big(\ln(z)\,2\Big)$ The iteration of $T$ is implemented in the following way: :$\!\!\!\!\!\!\!\!\!\!\ (2) ~ ~ ~y=T^n(x)={\mathrm{Pow}_2}^n(z)=F\Big(n+G(x)\Big)$ where : $\!\!\!\!\!\!\!\!\!\!\ (3) ~ ~ ~ F(z)=\exp\Big( \exp\big( \ln(2)\, z\big)\Big)$ is superfunction for the transfer function $T$ and :$\!\!\!\!\!\!\!\!\!\!\ (4) ~ ~ ~G(z)=\ln\Big( \ln(z) \Big)/ \ln(2)$ is the Abel Function. The thick lines represent $y=x^2$ and $y=\sqrt{x}$. FIrst of them overlaps with <matm>y=T^1(x)$ and corresponds to $c\!=\!1$, and the second overlaps with $y=T^{-1}(x)$ and corresponds to $c\!=\!-1$. |
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| Citizendium author & Copyright holder
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Copyright © Dmitrii Kouznetsov. See below for licence/re-use information. |
| Date created
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2012.11.11 |
| Country of first publication
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Japan |
| Notes
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| Other versions
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http://tori.ils.uec.ac.jp/TORI/index.php/File:PowIteT.jpg |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 19:52, 11 March 2022 | | 2,093 × 2,093 (1.01 MB) | Maintenance script (talk | contribs) | == Summary == Importing file |
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