03/12/2009, 12:32 AM
maybe this is trivial but i was thinking about iteration like
f_n+1(z) = log(f_n(z)^(p*q)) / (p*q)
where p and q are prime or 1.
e.g. iterations of
log(x^2)/2
log(x^3)/3
log(x^6)/6
i think the average of infinite iterations converges to
the value (p*q) * fixpoint of z = log(z)
for almost all z.
or something like that ...
just a quick idea ...
f_n+1(z) = log(f_n(z)^(p*q)) / (p*q)
where p and q are prime or 1.
e.g. iterations of
log(x^2)/2
log(x^3)/3
log(x^6)/6
i think the average of infinite iterations converges to
the value (p*q) * fixpoint of z = log(z)
for almost all z.
or something like that ...
just a quick idea ...