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 new results from complex dynamics bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 03/22/2010, 12:07 AM (This post was last modified: 03/22/2010, 12:10 AM by bo198214.) (03/21/2010, 11:03 PM)mike3 Wrote: So does this mean the original hypothesis that it "depends holomorphically on $b$" (apparently across $e^{1/e}$ since you contrast this behavior with that of the "usual" regular iteration) was wrong? Quite probably. I am still not sure about numeric computation of the bipolar Abel/super function. But my guess that it is not real valued for $b stems also from a statement in Shishikura's article (proposition 3.2.3) which quite resembles Dmitrii Kouznetsov's algorithm to compute the superfunction. It says that the inverse of the bipolar Abel function, i.e. the superfunction $\phi_f$ satisfies: $\lim_{\Im(w)\to +\infty}\phi_f(w) = p$ and $\lim_{\Im(w)\to -\infty} \phi_f(w) = q$ where $p$ and $q$ are the two fixed points of $f$. (which is exactly what Dmitrii uses for his construction of the superfunction.) This implies that $\phi_f$ is only real-valued if $\overline{p}=q$ because real-analytic functions $\phi$ satisfy $\overline{\phi(z)}=\phi(\overline{z})$. « Next Oldest | Next Newest »

 Messages In This Thread new results from complex dynamics - by bo198214 - 01/25/2010, 07:30 PM RE: new results from complex dynamics - by mike3 - 01/26/2010, 06:21 AM RE: new results from complex dynamics - by bo198214 - 03/08/2010, 11:59 AM RE: new results from complex dynamics - by mike3 - 03/10/2010, 03:10 AM RE: new results from complex dynamics - by bo198214 - 03/10/2010, 11:13 AM RE: new results from complex dynamics - by mike3 - 03/20/2010, 08:12 AM RE: new results from complex dynamics - by bo198214 - 03/21/2010, 01:04 PM RE: new results from complex dynamics - by mike3 - 03/21/2010, 11:03 PM RE: new results from complex dynamics - by bo198214 - 03/22/2010, 12:07 AM RE: new results from complex dynamics - by mike3 - 03/22/2010, 10:14 AM RE: new results from complex dynamics - by Gottfried - 03/22/2010, 01:32 PM RE: new results from complex dynamics - by bo198214 - 03/22/2010, 01:37 PM RE: new results from complex dynamics - by mike3 - 03/23/2010, 07:50 AM RE: new results from complex dynamics - by bo198214 - 03/23/2010, 10:32 AM RE: new results from complex dynamics - by bo198214 - 02/19/2013, 11:22 PM RE: new results from complex dynamics - by sheldonison - 02/20/2013, 05:25 AM RE: new results from complex dynamics - by sheldonison - 02/21/2013, 09:01 AM RE: new results from complex dynamics - by bo198214 - 02/24/2013, 08:57 PM RE: new results from complex dynamics - by sheldonison - 02/25/2013, 01:42 AM RE: new results from complex dynamics - by sheldonison - 03/21/2012, 08:58 PM RE: new results from complex dynamics - by sheldonison - 04/10/2012, 10:37 PM RE: new results from complex dynamics - by sheldonison - 04/15/2012, 04:30 PM RE: new results from complex dynamics - by mike3 - 04/16/2012, 04:21 AM RE: new results from complex dynamics - by mike3 - 04/17/2012, 07:51 AM RE: new results from complex dynamics - by sheldonison - 04/17/2012, 12:48 PM RE: new results from complex dynamics - by mike3 - 04/18/2012, 02:19 AM

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