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some questions about sexp
#12
more about those cycles and attractors :

you can find g that can't be written as f°f°...°f for any n > 1.
Namely, suppose g has exactly one fixed point p_0, and exactly one p_1 <> p_0 such that
g(p_1) = p_0, and at least one p_2 such that g(p_2) = p_1. If g = f°f°...°f, it's
easy to see that f(p_0) = p_0, f(p_1) = p_0, and (for some p_3) f(p_3) = p_1.
But then f(f(p_3)) = p_0 which would imply g(p_3) = p_0, contradiction.

A suitable g is g(x) = x + 2 - 2 exp(x).


hope that helps

regards

tommy1729
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Messages In This Thread
some questions about sexp - by tommy1729 - 06/28/2010, 11:18 PM
RE: some questions about sexp - by tommy1729 - 06/29/2010, 10:55 PM
RE: some questions about sexp - by bo198214 - 07/01/2010, 09:39 AM
RE: some questions about sexp - by mike3 - 07/01/2010, 11:05 AM
RE: some questions about sexp - by bo198214 - 07/02/2010, 07:14 AM
RE: some questions about sexp - by tommy1729 - 07/01/2010, 10:06 PM
RE: some questions about sexp - by mike3 - 07/01/2010, 10:28 PM
RE: some questions about sexp - by bo198214 - 07/02/2010, 07:17 AM
RE: some questions about sexp - by mike3 - 07/02/2010, 07:55 AM
RE: some questions about sexp - by tommy1729 - 07/02/2010, 12:27 PM
RE: some questions about sexp - by sheldonison - 07/02/2010, 03:52 PM
RE: some questions about sexp - by tommy1729 - 07/05/2010, 09:59 PM
RE: some questions about sexp - by sheldonison - 07/06/2010, 01:45 PM

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