Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
new results from complex dynamics
#6
(03/10/2010, 11:13 AM)bo198214 Wrote:
(03/10/2010, 03:10 AM)mike3 Wrote: Hmm. This suggests the possibility there is an alternative solution instead of regular iteration for the bases in (after all, if it's analytic at and the regular isn't, the two can't be equal if they're both analytic in that interval.).

Oh, my explanation was misunderstandable, the bipolar Abel function is always holomorphic and injective on a sickel between the two fixed points. But it may not be real on the real axis, or perhaps not even defined on the real axis, in the case of two real fixed points. You know the sickel would be above or below the real axis or possibly even wind around the fixed points, so being defined on pieces of the real axis; and it is not clear whether it can be extended to the real axis between the fixed points.

On the other hand to obtain alternative solutions you can always build up linear combinations of the two regular Abel functions , :
which is again an Abel function:

However, for it to be not real valued in and real valued in would imply there is a singularity/branchpoint at , hence not holomorphic there, eh?
Reply


Messages In This Thread
new results from complex dynamics - by bo198214 - 01/25/2010, 07:30 PM
RE: new results from complex dynamics - by mike3 - 01/26/2010, 06:21 AM
RE: new results from complex dynamics - by mike3 - 03/10/2010, 03:10 AM
RE: new results from complex dynamics - by mike3 - 03/20/2010, 08:12 AM
RE: new results from complex dynamics - by mike3 - 03/21/2010, 11:03 PM
RE: new results from complex dynamics - by mike3 - 03/22/2010, 10:14 AM
RE: new results from complex dynamics - by mike3 - 03/23/2010, 07:50 AM
RE: new results from complex dynamics - by mike3 - 04/16/2012, 04:21 AM
RE: new results from complex dynamics - by mike3 - 04/17/2012, 07:51 AM
RE: new results from complex dynamics - by mike3 - 04/18/2012, 02:19 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Complex Tetration, to base exp(1/e) Ember Edison 7 2,613 08/14/2019, 09:15 AM
Last Post: sheldonison
  THE problem with dynamics tommy1729 1 2,513 04/04/2017, 10:52 PM
Last Post: tommy1729
  Dynamics as alternating waves tommy1729 2 2,520 02/13/2017, 01:01 AM
Last Post: tommy1729
  An explicit series for the tetration of a complex height Vladimir Reshetnikov 13 13,029 01/14/2017, 09:09 PM
Last Post: Vladimir Reshetnikov
  Cyclic dynamics f(-x) = T (f(x)) tommy1729 2 2,723 08/25/2015, 08:23 AM
Last Post: tommy1729
  [2014] " statistical dynamics " tommy1729 0 1,823 08/31/2014, 11:53 PM
Last Post: tommy1729
  Negative, Fractional, and Complex Hyperoperations KingDevyn 2 6,563 05/30/2014, 08:19 AM
Last Post: MphLee
  Complex Tetration Balarka Sen 16 22,986 02/21/2013, 02:23 PM
Last Post: sheldonison
  (MSE) periods in (z*exp(z*exp(...))) for complex z Gottfried 0 2,962 04/16/2012, 10:24 AM
Last Post: Gottfried
  Real and complex behaviour of the base change function (was: The "cheta" function) bo198214 39 54,693 08/13/2011, 06:33 PM
Last Post: bo198214



Users browsing this thread: 1 Guest(s)