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 f(f(x)) = exp(x) + x mike3 Long Time Fellow Posts: 368 Threads: 44 Joined: Sep 2009 12/12/2009, 11:35 PM (This post was last modified: 12/12/2009, 11:39 PM by mike3.) I'm curious: where are the branch points for the positive-real-count fractional iterations such as $F^{1/2}(z)$ on the complex plane? I tried a graph on the complex plane for z in the square from -5-5i to +5+5i and I noticed two cutlines (at $t \pm i \pi$ it appears (where t is real)), but they seem to go across the entire plane. So are these "real", i.e. are there branch points on them (or outside the graphing square), or are they just an artifact of the algorithm and the fractional iterate is actually entire (i.e. we could analytically continue it out of the region near 0 into the whole plane)? « Next Oldest | Next Newest »

 Messages In This Thread f(f(x)) = exp(x) + x - by tommy1729 - 12/12/2009, 12:54 AM RE: f(f(x)) = exp(x) + x - by bo198214 - 12/14/2009, 09:52 AM RE: f(f(x)) = exp(x) + x - by tommy1729 - 12/14/2009, 09:47 PM

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