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 the inconsistency depending on fixpoint-selection Gottfried Ultimate Fellow Posts: 770 Threads: 120 Joined: Aug 2007 03/14/2008, 02:10 PM (This post was last modified: 03/14/2008, 02:15 PM by Gottfried.) Ok, I've fiddled some days with this case of iteration. Now new information, but lots of paper with interesting graphs... bo198214 Wrote:but at least we have traced back the regular iteration at different fixed points to the regular iteration of different scalings. Does this also work for higher order polynomials? Hmm, I haven't done this, because even if we get the coefficients linearly scaled this does not give obvious and special helpful interesting information when iterated. Also I doubt, that it can be done with higher polynomials - it was just computing a +/- deviance d of same abolute value of a sort of mean-value for the two fixpoints. If we have three or more, like f(x) = x + (x-t0)(x-t1)(x-t2) then in general there are no common d's with same absolute value - so I think, this will be impossible. However, this led me to rethink the formula derived from symbolic eigensystem-decomposition of the b^x-1 - iteration. Written as function of height parameter h it is something like $f_{b,x}(h) = a_{1_{x,u}}*u^h + a_{2_{x,u}}*u^{2h} + a_{3_{x,u}}*u^{3h} + ...$ (where u=log(b) and the a_k are functions of x and u, resp are constant for given x and u) which made me fiddle with the derivatives, sums of f(h) with increasing h (again) and so on. If I have news, I'll post it in the tetra-series thread. 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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