jaydfox Wrote:I wouldn't go so far as to say "no meaning", but certainly heuristic analysis can impute more meaning in a situation than is warranted at times.I just found it strange to say something "should" be that way if it mathematically (non changably) "is" this or that way. Its strange if it "should" be different from what it "is" and also strange, as in our case, if it "should" be the same that it "is".

Quote:As for pictures, I'm working on some.Yes, they would be really helpful. Though I can perceive your joy in the imagination of the mathematical situation, the picture remains somewhat vague, if not supported by something directly accessible.

And regarding Fourier analysis ... I was absent when this topic was tought Means I probably have to go back to the basics of it, before I can follow somewhat more sophistaced usage of it.

Quote:yet I would imagine that both satisfy the infinite matrix solution.

Yes the infinite matrix equation is just an other form of (i.e. equivalent to) the Abel equation. Every solution of the Abel equation is a solution to the matrix equation and vice versa.

By an e-mail conversation with Jean Ecalle it turns out that my conjecture was not completely true.

What however is true that

Quote:For each *entire* function the regular iterations at each two different fixed points are different.