bo198214 Wrote:I received an e-mail of Dan Asimov where he mentions that the continuous iterations of at the lower and upper real fixed points, , differ! He, Dean Hickerson and Richard Schroeppel found this arround 1991, however there is no paper about it.Henryk -

The numerical computations veiled this fact because the differences are in the order of . I reverified this by setting the computation exactness to 100 decimal digits and using the recurrence formula described here:

, where is the fixed point of and and .

I'm currently investigating the computation of the different eigenmatrices based on the different fixpoints. Apparently the computations lead to the same tetration-matrices Bs (or Bb) in the examples, where I checked this, and thus to the same coefficients for the exponential series (in column 2 of the constructed Bb-matrix). Now the above seems to say, they are in fact not equal. So I'd like to get more infos about the details of the problem. I could not translate your argument above into my matrix-concept - can you explain a bit more explicite? And: do you know some more arguments for the statement of a difference (unfortunately, Dan Asimov seems to have said, there are no papers available)?

Gottfried

Gottfried Helms, Kassel