11/04/2014, 09:39 AM
I wonder how the analogue pictures look like for exp(x).
regards
tommy1729
regards
tommy1729
Attempt to find a limit point but each step needs doubling the precision...
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11/04/2014, 09:39 AM
I wonder how the analogue pictures look like for exp(x).
regards tommy1729
11/04/2014, 12:01 PM
(11/03/2014, 11:40 PM)jaydfox Wrote: Gottfried, Hi Jay, that were wonderful images; I forgot to take a look at them. Sometimes I think we should try to compose some "paedagogical" workout of what we've really achieved here in the forum and the main links to the articles... Quote:I think, if you look at the pictures, that you will see that there are singularities, fanning out from the fixed point at real 4. To get to the real axis, you will have to navigate a course between the singularities. This is likely the cause of the slow convergence, as well as the need for high precision. Yes, I'm trying to get some more comprehension of this aspect. To get aware of singularities should help against wrong speculations... Gottfried
Gottfried Helms, Kassel
Upps, I think I'd mystified myself... and the properties in question are actually well known.
Recap what I've done: 1) I chose some 2) I mapped this numbers by the imaginary height-iteration by 3) Now my question was, what is the number 4) Well, what my procedures actually do (and what I did no more consider seriously) is (to allow use of the power series of the Schroeder-function) to iterate the value Hmm... what I was missing was, that the mapping around the lower fixpoint does nothing else than to find a (real!) value below 2. So in fact I chose one value That calls for sarcasm... I simply could have used the original We have that the interval This seems to be the simple answer; and my question, where the mapping of If that reasoning is correct so far, then we could also complete the white spaces in Jay's images by neighboured drop-shapes, all with their edge at real-positive infinity. If this is all correct, then... it was really so simple. ;-) Gottfried
Gottfried Helms, Kassel
11/04/2014, 10:56 PM
Hmm
Why does not every path become a loop ? Afterall we consider iterations in the direction of the period ? But for some reason we are talking about going to oo. regards tommy1729
I think the white space needs to be computed from the other 3 superfunctions.
It might be a uniqueness criterion if these new contours do not overlap with the older ones. Switching branches fails because we have a different functional equation at another branch ( as discussed with sheldon ). Its fascinating to apparantly see that the boundaries of the current pics are created by the higher fixpoints. Now you should be able to complete the pictures ! regards tommy1729
11/09/2014, 10:25 PM
See the recently created related thread
http://math.eretrandre.org/tetrationforu...hp?tid=933 regards tommy1729 |
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