Jabotinsky's iterative logarithm

[bo198214]

For finite matrices it is also known, that matrices are commuting, if their eigenvectors are identical. But if the eigenvectors are identical, then FM and GM differ only by their sets of eigenvalues FV and GV.

Thats a good additional information for us non-matrixers

Hmm. What is surprising now is, that if FM and GM provide different iterates, then, for tetration, the eigenvalues in FV and GV must be appropriate powers of the same base - this seems much more restrictive than the statement of Jabotinski: there I can't find such a restriction (but maybe I'm just missing this at the moment)

But take into account that Jabotinsky is only considering functions with f(0)=0, i.e. which have a fixed point at 0. Generally all formal powerseries co mputations are restricted to this case because otherwise the coefficients of composition are no finite expressions (in terms of power series coefficients) anymore.