File:PowIteT.jpg: Difference between revisions

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current	18:52, 11 March 2022		2,093 × 2,093 (1.01 MB)	Maintenance script (talk \| contribs)	== Summary == Importing file

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 == Summary ==
-{{Image_Details|user
+Importing file
-|description  = [[Explicit plot]] of <math>n</math>th Iteration of the quadratic function, id est, [[power function]] for power 2; <math>y=\mathrm{Pow}_2^{~n}(z)=T^n(x)~</math> for various values of number <math>n</math> 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  $c\!=\!-1$.
-|author       = [[User:Dmitrii Kouznetsov|Dmitrii Kouznetsov]]
-|date-created = 2012.11.11
-|pub-country  = Japan
-|notes        =
-|versions     = http://tori.ils.uec.ac.jp/TORI/index.php/File:PowIteT.jpg
-}}
-== Licensing ==
-{{CC|by|3.0}}