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 ...