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 tetration from alternative fixed point Daniel Fellow Posts: 91 Threads: 33 Joined: Aug 2007 12/24/2019, 06:26 AM I asked this question in 1993 in the following manner,  Consider two fixed points $\alpha_1, \alpha_2$ of the complex exponential map $a^z$ where $a^{\alpha_1}=\alpha_1$ and $a^{\alpha_2}=\alpha_2$ and their Lyapunov multipliers $\lambda_1, \lambda_2$.  Can the forward orbit of $a^z$ traverse a region of space dominated by $\alpha_1,\lambda_1$ to the region dominated by $\alpha_2,\lambda_2$? My numerical research indicated that the answer can be affirmative. The main problem I faced what the chaotic region between $\alpha_1, \alpha_2$. By adjusting $a\rightarrow 1$ the chaotic region becomes arbitrarily thin and several hundred iterations can map $\alpha_1,\lambda_1$ to $\alpha_2,\lambda_2$. « Next Oldest | Next Newest »

 Messages In This Thread tetration from alternative fixed point - by sheldonison - 05/23/2010, 12:05 AM RE: tetration from alternative fixed point - by bo198214 - 05/23/2010, 07:54 AM RE: tetration from alternative fixed point - by sheldonison - 05/24/2010, 04:41 AM RE: tetration from alternative fixed point - by bo198214 - 05/24/2010, 11:43 AM RE: tetration from alternative fixed point - by sheldonison - 05/24/2010, 03:03 PM RE: tetration from alternative fixed point - by sheldonison - 06/03/2010, 04:13 AM RE: tetration from alternative fixed point - by sheldonison - 06/21/2010, 04:24 PM RE: tetration from alternative fixed point - by bo198214 - 06/27/2010, 06:02 AM RE: tetration from alternative fixed point - by tommy1729 - 06/27/2010, 10:18 PM RE: tetration from alternative fixed point - by bo198214 - 06/28/2010, 03:08 AM RE: tetration from alternative fixed point - by sheldonison - 06/28/2010, 11:03 PM RE: tetration from alternative fixed point - by bo198214 - 06/29/2010, 06:53 AM RE: tetration from alternative fixed point - by sheldonison - 07/01/2010, 03:31 PM RE: tetration from alternative fixed point - by bo198214 - 07/02/2010, 07:37 AM RE: tetration from alternative fixed point - by bo198214 - 07/21/2010, 03:24 AM RE: tetration from alternative fixed point - by sheldonison - 07/21/2010, 04:58 PM RE: tetration from alternative fixed point - by sheldonison - 08/13/2010, 03:53 PM RE: tetration from alternative fixed point - by JmsNxn - 12/05/2011, 07:58 PM RE: tetration from alternative fixed point - by sheldonison - 12/06/2011, 02:43 PM RE: tetration from alternative fixed point - by Daniel - 12/24/2019, 06:26 AM

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