Assume some given holomorphic function T.
The superfunction is holomorphic solution F of equation
The Abel function (or abelfunction) is the inverse of superfunction,
The abelfunction is solution of the Abel equation
As the superfunction F and the abelfunction G=F-1 are established, the nth iterate of transfer function T can be expressed as follows:
This expression allows to evaluate the non-integer iterates. The number n of iterate can be real or even complex.
In particular, for integer n, the iterates have the common meaning:
T-1 is inverse function of T,
and so on. For complex m and n, the group property holds:
The book is about evaluation of the superfunction F, the abelfunction G and the non-integer iterates of various transfer function T.
The Russian version is also available at my site,
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