Quote:Lastly, it is also known that for analytic iteration to exist uniquely, that the function being iterated must have a hyperbolic fixed pointOut of curiosity, why did you exclude the possibility of a parabolic fixed point?
And what of functions with multiple (non-conjugate) fixed points? Would uniqueness depend on the existence of a single hyperbolic fixed point (or a single pair of conjugates)?
And PS, thanks for the links and ideas. Most of my formal and self-training is fairly narrowly concentrated on good old-fashioned number crunching and vector analysis. I have big holes in my understanding of more "basic" topics in topology, group theory, set theory, rings and fields, etc., so it's good to know that between the few of us in this forum, we'll be able to bounce ideas off each other and get guidance. For now, I'm down in the trenches studying your slog, and it's a fascinating thing to study, but I know I need to broaden out a little bit. I'm especially ignorant of the matrix methods (by that, I mean the carleman or bell or whatever matrices, can't remember the names at the moment).
~ Jay Daniel Fox