• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 new results from complex dynamics mike3 Long Time Fellow Posts: 368 Threads: 44 Joined: Sep 2009 01/26/2010, 06:21 AM (01/25/2010, 07:30 PM)bo198214 Wrote: In some other post on this forum I mentioned that the regular Abel function/regular iterate of $f(x)=b^x$ at the lower fixed point for $b is probably not holomorphically continuable in $b$ to $b=e^{1/e}$. However if one uses the perturbed Fatou coordinates for $b and not the regular ones at the lower fixed point, then it (and the resulting fractional iterates) depends holomorphically on $b$! I have to revalidate this statement, but it appears very promising. Do you have proof that this is the case? As this could mean the regular iteration is the "wrong" way to do tetration, not the "right" one. It would be interesting to compare the graph of tetration at some base, say $\sqrt{2}$, obtained through the regular iteration, to that obtained through this method, esp. on the complex plane, and also to determine the magnitude of the disagreement between the two at the real axis. « 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

 Possibly Related Threads... Thread Author Replies Views Last Post Complex or Real numbers more important? Daniel 0 131 12/22/2019, 10:36 AM Last Post: Daniel Complex Tetration, to base exp(1/e) Ember Edison 7 2,205 08/14/2019, 09:15 AM Last Post: sheldonison THE problem with dynamics tommy1729 1 2,389 04/04/2017, 10:52 PM Last Post: tommy1729 Dynamics as alternating waves tommy1729 2 2,384 02/13/2017, 01:01 AM Last Post: tommy1729 An explicit series for the tetration of a complex height Vladimir Reshetnikov 13 12,395 01/14/2017, 09:09 PM Last Post: Vladimir Reshetnikov Cyclic dynamics f(-x) = T (f(x)) tommy1729 2 2,619 08/25/2015, 08:23 AM Last Post: tommy1729 [2014] " statistical dynamics " tommy1729 0 1,757 08/31/2014, 11:53 PM Last Post: tommy1729 Negative, Fractional, and Complex Hyperoperations KingDevyn 2 6,378 05/30/2014, 08:19 AM Last Post: MphLee Complex Tetration Balarka Sen 16 22,321 02/21/2013, 02:23 PM Last Post: sheldonison (MSE) periods in (z*exp(z*exp(...))) for complex z Gottfried 0 2,884 04/16/2012, 10:24 AM Last Post: Gottfried

Users browsing this thread: 1 Guest(s)