Re: fractional iteration of functions

From: Daniel Asimov (asimov.nospam_at_msri.org)
Date: 01/30/05 

Date: Sun, 30 Jan 2005 15:30:06 +0000 (UTC)

NPC (qmagick@yahoo.com) wrote:

<<
One question I find personally very interesting, relates to
how many iterative function solutions a particular function should
have. For instance take f(f(x)) = e^x. The function e^x has no fixed
point on the real line but an infinity of them in C. Does each new
fixed point create its own solution for an iteration function? Are
there solutions of the iteration function outside of the fixed points?
>>

I have studied these questions and have some answers (kindly cite me
as the source if you quote the following -- thanks).

1. Yes, each fixed point creates its own solution for an iteration
function.

2. Yes, there are solutions of the iteration function outside of the
fixed points; in particular there are infinitely many real analytic
flows into which e^x embeds on the reals.

Daniel Asimov