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 tetration from alternative fixed point sheldonison Long Time Fellow Posts: 638 Threads: 22 Joined: Oct 2008 08/13/2010, 03:53 PM (This post was last modified: 08/13/2010, 04:01 PM by sheldonison.) (06/28/2010, 11:03 PM)sheldonison Wrote: ....To generate these contours lines in the SuperFunction, I used the inverse super function with img(z)=-3pi*i contour with real(z) varying from $+/-\infty$. Then I graph the exponent of that contour line, which is repeated one unit away, with img(z)=0 and real(z) varying from -$\infty$ to 0, and the exponent of that contour line with img(z)=0 and real(z) varying from 0..1. The three contours are disconnected from each other, which I think you were pointing out to begin with. The Reimann mapping will not be analytic at the boundary points. .... - Sheldon The complex periodicity is incorrect in this graph, which effects the "alternative 3*pi*i contour" graph. For the period I incorrectly used: period = 2Pi*i/L The correct value is period = 2Pi*i/(L-2*Pi*I) This is because the correct equation for the periodiicty is 2*Pi*i/ln(L) Because L>2Pi*I, the primary ln(L)=L-2*Pi*I. The correct complex period=1.3769+2.1751*I. I haven't verified the rest of the graph, but otherwise, I'm still using the same equations as I used when I made this graph, and those equations should have given correct values for the other complex contours. By the way, the equations are posted here. I found the problem when I wrote a pari-gp script for the secondary fixed point. With the fix, the alternative contour no longer fits snugly against the primary i=0 contour. I'm still interested in seeing if there's any way to Riemann map the contours back to a well defined real axis, but I still assume that it is not possible. - Sheldon « Next Oldest | Next Newest »

 Messages In This Thread tetration from alternative fixed point - by sheldonison - 05/23/2010, 12:05 AM RE: tetration from alternative fixed point - by bo198214 - 05/23/2010, 07:54 AM RE: tetration from alternative fixed point - by sheldonison - 05/24/2010, 04:41 AM RE: tetration from alternative fixed point - by bo198214 - 05/24/2010, 11:43 AM RE: tetration from alternative fixed point - by sheldonison - 05/24/2010, 03:03 PM RE: tetration from alternative fixed point - by sheldonison - 06/03/2010, 04:13 AM RE: tetration from alternative fixed point - by sheldonison - 06/21/2010, 04:24 PM RE: tetration from alternative fixed point - by bo198214 - 06/27/2010, 06:02 AM RE: tetration from alternative fixed point - by tommy1729 - 06/27/2010, 10:18 PM RE: tetration from alternative fixed point - by bo198214 - 06/28/2010, 03:08 AM RE: tetration from alternative fixed point - by sheldonison - 06/28/2010, 11:03 PM RE: tetration from alternative fixed point - by bo198214 - 06/29/2010, 06:53 AM RE: tetration from alternative fixed point - by sheldonison - 07/01/2010, 03:31 PM RE: tetration from alternative fixed point - by bo198214 - 07/02/2010, 07:37 AM RE: tetration from alternative fixed point - by bo198214 - 07/21/2010, 03:24 AM RE: tetration from alternative fixed point - by sheldonison - 07/21/2010, 04:58 PM RE: tetration from alternative fixed point - by sheldonison - 08/13/2010, 03:53 PM RE: tetration from alternative fixed point - by JmsNxn - 12/05/2011, 07:58 PM RE: tetration from alternative fixed point - by sheldonison - 12/06/2011, 02:43 PM RE: tetration from alternative fixed point - by Daniel - 12/24/2019, 06:26 AM

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