Difference between revisions of "Schröder iterate"
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$$f^t(z)=\lim_{n\to\infty} f^{-n}(c_1^t f^n(z))$$ | $$f^t(z)=\lim_{n\to\infty} f^{-n}(c_1^t f^n(z))$$ | ||
| − | Or $\sigma$ being the [[Schröder | + | Or $\sigma$ being the [[Schröder coordinate]] of $f$ at $a$, we have: |
$$f^t(z)=\sigma^{-1}(c_1^t \sigma(z))$$ | $$f^t(z)=\sigma^{-1}(c_1^t \sigma(z))$$ | ||
Latest revision as of 08:39, 8 June 2011
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: $$f^t(z)=\sigma^{-1}(c_1^t \sigma(z))$$