fractional iterate of x ?

[tommy1729]

I think a keyword here is "babbage equation".
Its thoroughly described for example in Kuczma's book "Iterative functional equations".
Though I mainly forgot about it, its about functional roots of the identity function.

perhaps.

its intresting , but in essence only deals with half-iterates.

i couldnt find anything free on the internet of any value.

im not an expert in "babbage math" , but i believe he used the matrices too , or am i wrong ?

i would love to learn more about this mysterious babbage equation...

regards

tommy1729