Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
[UFO] Attracting Fixpoints or attracting line?
#11
(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 , 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 ; and found that the corresponding "fixed points" lie smoothly on a line between the proper fixed points of .

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 ?
Reply


Messages In This Thread
RE: [UFO] Attracting Fixpoints or attracting line? - by tommy1729 - 04/09/2010, 12:11 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Merged fixpoints of 2 iterates ? Asymptotic ? [2019] tommy1729 1 126 09/10/2019, 11:28 AM
Last Post: sheldonison
  b^b^x with base 0<b<e^-e have three real fixpoints Gottfried 1 1,999 11/07/2017, 11:06 AM
Last Post: sheldonison
  Is the straight line the shortest, really? Xorter 0 1,172 05/23/2017, 04:40 PM
Last Post: Xorter
  2 fixpoints , 1 period --> method of iteration series tommy1729 0 1,266 12/21/2016, 01:27 PM
Last Post: tommy1729
  2 fixpoints related by power ? tommy1729 0 1,269 12/07/2016, 01:29 PM
Last Post: tommy1729
  2 real fixpoints again ....... tommy1729 10 8,159 02/23/2016, 10:17 PM
Last Post: tommy1729
  Fixpoints a,b with f ' (a) = f ' (b) = 1 tommy1729 0 1,478 09/15/2015, 08:29 AM
Last Post: tommy1729
  alternative fixpoints = branches ? tommy1729 0 1,584 10/11/2014, 08:50 AM
Last Post: tommy1729
  Wild conjecture about 2 fixpoints. tommy1729 0 1,669 05/03/2014, 10:56 PM
Last Post: tommy1729
  The mystery of 2 fixpoints. tommy1729 0 1,461 05/03/2014, 10:11 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)