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 the inconsistency depending on fixpoint-selection Gottfried Ultimate Fellow Posts: 758 Threads: 117 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

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