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 Bummer! bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 11/06/2007, 02:06 PM (This post was last modified: 11/06/2007, 02:09 PM by bo198214.) jaydfox Wrote:I haven't yet tried shifting the system before solving, though I suppose it's possible in principle, and I'd be curious to see if it worked. The mental gymnastics involved to derive the system prior to solving are a bit beyond me this morning (I hardly slept), so I'd have to think about it this evening. Oh, shifting is another interesting topic. What happens if we develop the series for $b^x$ (or more simple for $e^x$) not at 0 but at some other point $c$, then derive the slog and compare the back shiftet slog with the original slog. To see whether the method is independent on the development point. The easiest way is by considering the shifted conjugate: $g(x)=e^{x+c}-c$ as its iteration is $g^{\circ t}(x)=\exp^{\circ t}(x+c)-c$. So if we solve $\gamma(g(x))=\gamma(x)+1$ this translates to $\gamma(e^{x+c}-c)=\gamma(x)+1$ $\gamma\circ\tau_{-c}\circ\exp\circ\tau_{c}=\tau_1\circ \gamma$ $\gamma\circ\tau_{-c}\circ\exp=\tau_1\circ \gamma\circ\tau_{c}$ $\gamma\circ\tau_{-c}\circ\exp=\tau_1\circ \gamma\circ\tau_{-c}$ This means whenever we have a solution $\alpha$ of $\alpha(e^x)=\alpha(x)+1$ then we have a solution $\gamma(x)=\alpha(x+c)$ to the equation $\gamma(e^{x+c}-c)=\gamma(x)+1$. And the question is whether if $\alpha$ is the natural Abel function (Andrew's method) for the first equation, whether then $\alpha(x+c)$ is the natural Abel function for the second equation. Or in other words if $\gamma$ is the natural Abel function for the second equation whether then $\gamma(x-c)$ is the natural Abel function for the first equation. The power series development of $e^{x+c}-c=e^ce^x-c$ is just a linear combination of the powerseries development of $e^x$. « Next Oldest | Next Newest »

 Messages In This Thread Bummer! - by bo198214 - 10/05/2007, 10:18 AM RE: Bummer! - by Gottfried - 10/05/2007, 10:56 AM RE: Bummer! - by bo198214 - 10/05/2007, 11:17 AM RE: Bummer! - by bo198214 - 10/06/2007, 07:05 AM RE: Bummer! - by bo198214 - 10/06/2007, 09:18 AM RE: Bummer! - by nuninho1980 - 05/29/2011, 09:37 PM RE: Bummer! - by bo198214 - 05/29/2011, 10:11 PM RE: Bummer! - by nuninho1980 - 05/30/2011, 01:13 AM RE: Bummer! - by sheldonison - 05/30/2011, 03:25 PM RE: Bummer! - by bo198214 - 05/31/2011, 09:05 AM RE: Bummer! - by JmsNxn - 05/31/2011, 09:06 PM RE: Bummer! - by sheldonison - 06/01/2011, 03:03 AM RE: Bummer! - by bo198214 - 06/01/2011, 01:16 PM RE: Bummer! - by jaydfox - 10/07/2007, 04:26 PM RE: Bummer! - by bo198214 - 10/07/2007, 06:16 PM RE: Bummer! - by jaydfox - 10/07/2007, 07:48 PM RE: Bummer! - by jaydfox - 10/15/2007, 08:36 PM RE: Bummer! - by bo198214 - 11/02/2007, 08:30 PM RE: Bummer! - by jaydfox - 11/02/2007, 10:31 PM RE: Bummer! - by bo198214 - 11/02/2007, 11:06 PM RE: Bummer! - by jaydfox - 11/07/2007, 02:22 PM RE: Bummer! - by bo198214 - 11/07/2007, 02:27 PM RE: Bummer! - by jaydfox - 11/26/2007, 04:37 PM RE: Bummer! - by jaydfox - 11/04/2007, 02:24 AM RE: Bummer! - by bo198214 - 11/06/2007, 11:33 AM RE: Bummer! - by jaydfox - 11/04/2007, 02:32 AM RE: Bummer! - by jaydfox - 11/06/2007, 01:34 PM RE: Bummer! - by bo198214 - 11/06/2007, 02:06 PM RE: Bummer! - by Gottfried - 11/07/2007, 08:32 AM RE: Bummer! - by jaydfox - 11/08/2007, 02:16 AM RE: Bummer! - by bo198214 - 11/08/2007, 01:14 PM RE: Bummer! - by jaydfox - 11/09/2007, 04:59 AM RE: Bummer! - by jaydfox - 11/09/2007, 05:12 AM RE: Bummer! - by bo198214 - 11/12/2007, 08:45 PM RE: Bummer! - by jaydfox - 11/13/2007, 08:36 AM RE: Bummer! - by jaydfox - 11/09/2007, 07:04 AM RE: Bummer! - by jaydfox - 11/13/2007, 01:47 AM RE: Bummer! - by bo198214 - 11/13/2007, 10:36 AM RE: Bummer! - by jaydfox - 11/13/2007, 02:23 PM RE: Bummer! - by bo198214 - 11/13/2007, 02:41 PM Bummer conclusio - by bo198214 - 03/12/2008, 09:20 PM RE: Bummer! - by Kouznetsov - 04/18/2009, 12:46 PM RE: Bummer! - by andydude - 04/21/2009, 08:28 PM RE: Bummer! - by bo198214 - 04/21/2009, 09:02 PM RE: Bummer! - by andydude - 04/22/2009, 11:33 PM RE: Bummer! - by bo198214 - 04/23/2009, 08:39 AM RE: Bummer! - by bo198214 - 04/23/2009, 09:01 AM RE: Bummer! - by Kouznetsov - 04/18/2009, 11:24 AM regular iteration at two different fixed points - by bo198214 - 06/19/2009, 08:51 AM RE: regular iteration at two different fixed points - by Kouznetsov - 06/19/2009, 11:41 AM RE: regular iteration at two different fixed points - by bo198214 - 06/19/2009, 12:30 PM

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