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 regular iteration of sqrt(2)^x (was: eta as branchpoint of tetrational) Gottfried Ultimate Fellow Posts: 765 Threads: 119 Joined: Aug 2007 06/15/2011, 12:27 PM (06/09/2011, 06:20 PM)JmsNxn Wrote: Therefore how do we generate $\exp_{\sqrt{2}}^{\circ \sigma}(z)\,\,;\,\,\R(z) \in (2, 4)$? Do we create a middle super function? Beginning at x=1 we use the lower fixpoint (at 2) and the iterates are always between -infty and 2. if we begin at x=3 the iterates are always between 2 and 4. However, we can connect the two areas. If we begin at x=1 and iterate with the complex height h=0 + 2*Pi*i/log(log(2)) then we get exactly one value in the 2..4 interval. That is that we just switch the sign of the value of the schröder-function from positive to negative (one half round in the complex plane). That makes it also possible to define a "norm"-height for that values in the 2..4-interval. We set the real part of the height = 0 where x=1 was mapped to. Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Messages In This Thread regular iteration of sqrt(2)^x (was: eta as branchpoint of tetrational) - by JmsNxn - 06/09/2011, 06:20 PM RE: regular iteration of sqrt(2)^x (was: eta as branchpoint of tetrational) - by bo198214 - 06/09/2011, 07:16 PM RE: regular iteration of sqrt(2)^x (was: eta as branchpoint of tetrational) - by sheldonison - 06/09/2011, 07:49 PM RE: regular iteration of sqrt(2)^x (was: eta as branchpoint of tetrational) - by JmsNxn - 06/09/2011, 11:04 PM RE: regular iteration of sqrt(2)^x (was: eta as branchpoint of tetrational) - by sheldonison - 06/09/2011, 11:45 PM RE: regular iteration of sqrt(2)^x (was: eta as branchpoint of tetrational) - by Gottfried - 06/15/2011, 12:27 PM

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