https://tetrationforum.org/hyperops_wiki/index.php?action=history&feed=atom&title=B%C3%B6ttcher_iterateBöttcher iterate - Revision history2026-05-13T16:04:28ZRevision history for this page on the wikiMediaWiki 1.35.8https://tetrationforum.org/hyperops_wiki/index.php?title=B%C3%B6ttcher_iterate&diff=132&oldid=prevBo198214: first draft2011-06-08T08:38:22Z<p>first draft</p>
<p><b>New page</b></p><div>A way to compute the regular iterates of a function $f$ with [[super-attracting fixpoint]] $a$.<br />
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For $f(z)=c_m (z-a)^m + c_{m+1} (z-a)^{m+1} + \dots$ the Böttcher iterate is:<br />
$$f^t(z)=\lim_{n\to\infty} f^{-n}(f^n(z)^{m^t})$$<br />
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Or if $\beta$ is the [[Böttcher coordinate]] of $f$ at $a$, then <br />
$$f^t(z)=\beta^{-1}\left(\beta(z)^{m^t}\right)$$</div>Bo198214