11/12/2007, 11:52 AM

Gottfried Wrote:Hmm, this point disppeared for me, when I read your post first time.

So I could say, that this is already fixed, what I always called "my hypothesis about the set of eigenvalues"?

For the infinite case it is clear (by the existence of Schroeder functions at the fixed points), that \( \{\ln(a)^n: n\in\mathbb{N}\} \) is a set of Eigenvalues of \( B_b \) for each fixed point \( a \).

Quote:Further it may then be interesting to develop arguments for the degenerate case... In my "increasing size" (of the truncated Bell-matrix) analyses the courious aspect for base \( b= \eta \), appeared, that the set of eigenvalues show decreasing distances between them but also new eigenvalues pop up, and each new eigenvalue was smaller than the previous. See page "Graph"So there are concurring tendencies - and it may be fruitful to do an analysis, why this/how this could be compatible with the/a limit case, where they are assumed to approach 1 asymptotically.I really have no idea about the structure of Eigenvalues of truncations in this case. But somehow the non-integer iterations seem to converge in this case too (?)