https://tetrationforum.org/hyperops_wiki/index.php?action=history&feed=atom&title=Fatou_coordinate 2026-05-13T15:11:34Z Revision history for this page on the wiki MediaWiki 1.35.8 https://tetrationforum.org/hyperops_wiki/index.php?title=Fatou_coordinate&diff=98&oldid=prev 2011-06-05T14:52:45Z

<p>removed plural s</p> <table class="diff diff-contentalign-left diff-editfont-monospace" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 14:52, 5 June 2011</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'>−</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Fatou <del class="diffchange diffchange-inline">coordinates </del>- a term predominantly used in [[holomorphic dynamics]] - usually refers to one of the $2m$ [[principal Abel function]]s of a holomorphic function $f$ with [[parabolic fixpoint]] (which we assume for simplicity to be located at 0):</div></td><td class='diff-marker'>+</td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Fatou <ins class="diffchange diffchange-inline">coordinate </ins>- a term predominantly used in [[holomorphic dynamics]] - usually refers to one of the $2m$ [[principal Abel function]]s of a holomorphic function $f$ with [[parabolic fixpoint]] (which we assume for simplicity to be located at 0):</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>$$f(z)=z+c_{m+1}z^{m+1} + c_{m+2}z^{m+2} + \dots $$</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>$$f(z)=z+c_{m+1}z^{m+1} + c_{m+2}z^{m+2} + \dots $$</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Literature ==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Literature ==</div></td></tr> <tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Milnor, J. (2006). Dynamics in one complex variable. 3rd ed. Princeton Annals in Mathematics 160. Princeton, NJ: Princeton University Press. viii, 304 p.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Milnor, J. (2006). Dynamics in one complex variable. 3rd ed. Princeton Annals in Mathematics 160. Princeton, NJ: Princeton University Press. viii, 304 p.</div></td></tr> </table>

Bo198214 https://tetrationforum.org/hyperops_wiki/index.php?title=Fatou_coordinate&diff=97&oldid=prev 2011-06-05T14:51:30Z

<p>moved from plural</p> <p><b>New page</b></p><div>Fatou coordinates - a term predominantly used in [[holomorphic dynamics]] - usually refers to one of the $2m$ [[principal Abel function]]s of a holomorphic function $f$ with [[parabolic fixpoint]] (which we assume for simplicity to be located at 0):<br /> $$f(z)=z+c_{m+1}z^{m+1} + c_{m+2}z^{m+2} + \dots $$<br /> <br /> == Literature ==<br /> * Milnor, J. (2006). Dynamics in one complex variable. 3rd ed. Princeton Annals in Mathematics 160. Princeton, NJ: Princeton University Press. viii, 304 p.</div>

Bo198214