fractional iterate of x ?

[tommy1729]

i couldnt find much usefullness in relation to babbage's equation ...

but perhaps you would like to know what i wrote elsewhere :

assuming it is correct : quote :

i wrote :

> potentially unsolved : period of superfunction ?
>
> this thread reminds me of tetration and related ...
>
> i have explained how to compute the period of a
> taylor series.
>
> but how does one compute the period of the
> superfunction of a taylor series , without knowing
> the taylor series of the superfunction ???
>
> for those unfamiliar :
>
> superfunction[f(x)] = F(x) <=> F(x+1) = f(F(x))
>
>
> regards
>
> tommy1729

basicly if F(x) has a real period > 1 then :

T( (-1)^(2/P) inverseT(x) ) = f(x)

has a solution for T and a period P.

the smallest period P is then the period.

But is finding T easier than finding F ??

...euh...


tommy1729

( end quote )

regards

tommy1729