• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 the inconsistency depending on fixpoint-selection Gottfried Ultimate Fellow Posts: 770 Threads: 120 Joined: Aug 2007 03/07/2008, 09:38 PM (This post was last modified: 03/07/2008, 09:46 PM by Gottfried.) bo198214 Wrote:However your second transformation $x' = -4 x +1$, $x'' = -\frac{1}{4} x + \frac{1}{4}$, $g_1(x)=f(x'')'$ has as translation $\tau(x)=x+\frac{1}{4}$ the same translation as in your previous transformation! Only $\mu$ changes to $\mu(x)=-\frac{1}{4}x$. So this second transformation moves also the *greater* fixed point to 0. And we have seen that we can dismiss any multiplicative conjugation $\mu^{-1}\circ f\circ \mu$ with respect to regular iteration. So it has of course the same result (fractional iteration of $f$) as your first transformation. Yepp - I just found the position of the error, grmmpff. It is in Code:´ using e1=1/4                                e2 = -1/4         d1=1/4 / e1 =1                        d2 = 1/4 / e2 = -1 x' =  4x - 1                               x´ = -4x + 1 x" =  (x+1)/4                              x´´= (x-1)/-4 Although I had already that not e or d, but e*d = fixpoint, in the computation of d2, I used the same (1/4) as for d1. For clarity, I should have written a symbol for the selected fixpoint: Code:´ involving fixpoint p=1/4                    fixpoint q=-1/4 using e1=1/4                                e2 = -1/4         d1=p / e1 =1                          d2 = q / e2 = 1 x' =  4x - 1                               x´ = -4x - 1 x" =  (x+1)/4                              x´´= (x+1)/-4 Hope this corrects things, didn't check it again yet, but it seems that this reflects just the simple sign-changing in the matrices. The previous G2-matrix and the subsequent considerations in that posting are on a false assumption... Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Messages In This Thread the inconsistency depending on fixpoint-selection - by Gottfried - 02/07/2008, 03:06 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 02/07/2008, 05:20 PM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/04/2008, 10:14 AM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/04/2008, 11:17 AM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/04/2008, 11:25 AM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/04/2008, 11:32 AM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/04/2008, 11:43 AM RE: the inconsistency depending on fixpoint-selection - by GFR - 02/07/2008, 09:02 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 02/07/2008, 09:49 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/03/2008, 11:20 AM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/06/2008, 04:06 PM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/06/2008, 04:58 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/06/2008, 05:25 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/07/2008, 03:16 AM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/07/2008, 10:56 AM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/07/2008, 07:17 PM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/07/2008, 08:30 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/07/2008, 09:38 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/08/2008, 01:22 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/08/2008, 01:52 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/08/2008, 04:21 PM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/09/2008, 09:30 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/14/2008, 02:10 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/14/2008, 04:41 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/14/2008, 07:19 PM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 04/29/2008, 08:15 AM

 Possibly Related Threads... Thread Author Replies Views Last Post Iteration exercises: f(x)=x^2 - 0.5 ; Fixpoint-irritation... Gottfried 23 42,372 10/20/2017, 08:32 PM Last Post: Gottfried (Again) fixpoint outside Period tommy1729 2 4,032 02/05/2017, 09:42 AM Last Post: tommy1729 Polygon cyclic fixpoint conjecture tommy1729 1 3,371 05/18/2016, 12:26 PM Last Post: tommy1729 The " outside " fixpoint ? tommy1729 0 2,193 03/18/2016, 01:16 PM Last Post: tommy1729 2 fixpoint pairs [2015] tommy1729 0 2,524 02/18/2015, 11:29 PM Last Post: tommy1729 [2014] The secondary fixpoint issue. tommy1729 2 5,122 06/15/2014, 08:17 PM Last Post: tommy1729 Simple method for half iterate NOT based on a fixpoint. tommy1729 2 4,845 04/30/2013, 09:33 PM Last Post: tommy1729 2 fixpoint failure tommy1729 1 3,834 11/13/2010, 12:25 AM Last Post: tommy1729 abs f ' (fixpoint) = 0 tommy1729 2 6,025 09/09/2010, 10:13 PM Last Post: tommy1729 [Regular tetration] [Iteration series] norming fixpoint-dependencies Gottfried 11 18,561 08/31/2010, 11:55 PM Last Post: tommy1729

Users browsing this thread: 2 Guest(s)