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 the inconsistency depending on fixpoint-selection bo198214 Administrator Posts: 1,412 Threads: 91 Joined: Aug 2007 03/09/2008, 09:30 PM Gottfried Wrote:I tried to find one e, for which the resulting powerseries are linear scalings of each other, such that g0(x)=c * g1(x) This is possible. Assume again, that, denoting the fixpoints p and q, such that f(x) = x + (x - p) (x - q) Denote also the substitution z = x' = x/e - d and the backsubstitution x" = (x + d)*e Recall, that for a fixpoint p, d and e must be selected that p = e*d If I select Code:ยด     e0 = 1 + (p-q)    d0=p/e0          // first fixpoint     e1 = 1 + (q-p)    d1=q/e1          // second fixpointthen the resulting G0 and G1-matrices provide the same powerseries with a linear scaling. Ok, short verification: \begin{align*} g_0(x)&=f(x'')'\\ &=(x''+(x''-p)(x''-q))'\\ &=(xe_0+p + (xe_0+p-p)(xe_0+p-q))'\\ &=\frac{xe_0+e_0d + (xe_0)(xe_0+p-q)}{e_0} - d \\ &= x+x(xe_0+p-q)\\ &= x^2e_0 + x(1+p-q) = e_0(x^2+x) \end{align*} $g_1(x)=e_1(x^2+x)$ right. Thats indeed interesting. Quote:Anyway- this does not (yet?) provide a linear scaling for the half-powers Yes and thats the critical point here. There is no such law like $(cf)^{\circ t}=c^tf^{\circ t}$ 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? « 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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