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 [UFO] Attracting Fixpoints or attracting line? tommy1729 Ultimate Fellow Posts: 1,372 Threads: 336 Joined: Feb 2009 04/09/2010, 12:11 PM (04/09/2010, 06:43 AM)bo198214 Wrote: (04/08/2010, 10:03 PM)tommy1729 Wrote: your plot gives the fixed points of exp( t_k + k2pi i ) = t_k but should that not be periodic with k ? since exp( x + k i ) is periodic with real k ? im a bit confused now ... No, the fixed points of exp, i.e. the points with exp(z)=z, can be obtained by considering $z=\log(z)+2\pi i k$, $k\in\mathbb{Z}$ i.e. the fixed points of the branches of the logarithm. All the non-real fixed points of exp are repelling, i.e. |exp(z)|>1, thats why these fixed points are attracting for the logarithm and can be obtained by iterating the corresponding branch. Gottfried's question was now what happens if we choose non-integer $k$; and found that the corresponding "fixed points" lie smoothly on a line between the proper fixed points of $k\in\mathbb{Z}$. well , Bo , apart from the " no " i agree on what you said. in fact i already understood that. however , isnt t_k the same for e.g. k = 2 and k = 4 in the fixed points of exp( t_k + k2pi i ) = t_k ? « Next Oldest | Next Newest »

 Messages In This Thread [UFO] Attracting Fixpoints or attracting line? - by Gottfried - 02/22/2010, 08:31 PM RE: [UFO] Attracting Fixpoints or attracting line? - by bo198214 - 02/24/2010, 11:16 AM RE: [UFO] Attracting Fixpoints or attracting line? - by Gottfried - 02/24/2010, 02:31 PM RE: [UFO] Attracting Fixpoints or attracting line? - by Gottfried - 04/02/2010, 12:40 PM RE: [UFO] Attracting Fixpoints or attracting line? - by tommy1729 - 04/07/2010, 04:02 PM RE: [UFO] Attracting Fixpoints or attracting line? - by tommy1729 - 04/08/2010, 10:03 PM RE: [UFO] Attracting Fixpoints or attracting line? - by bo198214 - 04/09/2010, 06:43 AM RE: [UFO] Attracting Fixpoints or attracting line? - by tommy1729 - 04/09/2010, 12:11 PM RE: [UFO] Attracting Fixpoints or attracting line? - by bo198214 - 04/09/2010, 04:13 PM RE: [UFO] Attracting Fixpoints or attracting line? - by tommy1729 - 04/10/2010, 12:07 PM RE: [UFO] Attracting Fixpoints or attracting line? - by bo198214 - 04/10/2010, 09:45 PM RE: [UFO] Attracting Fixpoints or attracting line? - by tommy1729 - 04/19/2010, 11:36 PM RE: [UFO] Attracting Fixpoints or attracting line? - by tommy1729 - 02/27/2010, 11:11 PM RE: [UFO] Attracting Fixpoints or attracting line? - by Gottfried - 02/27/2010, 11:53 PM RE: [UFO] Attracting Fixpoints or attracting line? - by tommy1729 - 02/28/2010, 12:28 AM RE: [UFO] Attracting Fixpoints or attracting line? - by Gottfried - 04/09/2010, 08:30 PM RE: [UFO] Attracting Fixpoints or attracting line? - by tommy1729 - 04/10/2010, 12:25 PM RE: [UFO] Attracting Fixpoints or attracting line? - by tommy1729 - 04/27/2010, 11:06 PM

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