(editing remark: I changed the title or the original posting because of the contents of my current post in which I establish the connection between Regular iteration and the matrix-Jordan-form and give also a couple of online references)

Hi -

in answering a question in mathoverflow concerning a sequence of numbers given in OEIS (http://oeis.org/A008826), which are somehow related to fractional iteration for the f(x) = exp(x)-1 I found a surprising coincidence :

http://mathoverflow.net/questions/133593...281#151281

I've no further explanation so far, but it is interesting that the Jordan-form gives access to a variant of the Schröder-function to implement fractional iteration which was only possible with the matrix-logarithm (in that whole framework of the matrix-concept).

Perhaps I can say something more soon.

Gottfried

Hi -

in answering a question in mathoverflow concerning a sequence of numbers given in OEIS (http://oeis.org/A008826), which are somehow related to fractional iteration for the f(x) = exp(x)-1 I found a surprising coincidence :

http://mathoverflow.net/questions/133593...281#151281

I've no further explanation so far, but it is interesting that the Jordan-form gives access to a variant of the Schröder-function to implement fractional iteration which was only possible with the matrix-logarithm (in that whole framework of the matrix-concept).

Perhaps I can say something more soon.

Gottfried

Gottfried Helms, Kassel