Schröder iterate

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A way to compute regular iterates of a function $f$ with attracting or hyperbolic fixpoint $a$.

For $z$ in the immediate basin of attraction of the attracting fixpoint $a$ and $f'(a)=c_1$, it is: $$f^t(z)=\lim_{n\to\infty} f^{-n}(c_1^t f^n(z))$$

Or $\sigma$ being the Schröder coordinate of $f$ at $a$, we have: $$f^t(z)=\sigma^{-1}(c_1^t \sigma(z))$$