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Universal uniqueness criterion?
#36
(06/21/2009, 05:28 PM)Tetratophile Wrote: I said that the superlogarithm should be negative infinity at the fixed points,

No, its not. The super-exponential approaches L for , . Thatswhy the super-logarithm has positively unbounded imaginary part, if we approach the upper fixed point in the initial region, which one could interpret as . And it has negatively unbounded imaginary when we approach in the initial region which we could interpret as . However strictly considered there is no as value of a limit.

Quote: instead of infinity*i or = -infinity*i, because the fixed point is approached via a complex iteration, and then infinite negative iteration of exp, ie iteration of log.
If you approach the fixed point via repeated logarithm, then you dont stay inside the initial region.

Quote:
'bo198214 Wrote:I guess its about deforming one initial region into the other initial region
How do we go about doing that? It is not given whether the Abel functions are holomorphic outside of their domains.
If you go slightly to the right of having a curve inside then you can continue to the region between and , i.e. where we use the already established values of on the region between and .

This works if is bijective in the considered area. For example is bijective in the strip along the real axis , which includes the fixed points and .
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Messages In This Thread
Universal uniqueness criterion? - by bo198214 - 05/21/2008, 06:24 PM
RE: Universal uniqueness criterion? - by andydude - 05/22/2008, 05:19 AM
RE: Universal uniqueness criterion? - by andydude - 05/22/2008, 06:42 AM
RE: Universal uniqueness criterion? - by bo198214 - 05/22/2008, 11:25 AM
RE: Universal uniqueness criterion? - by andydude - 05/22/2008, 03:11 PM
RE: Universal uniqueness criterion? - by bo198214 - 05/22/2008, 05:55 PM
RE: Universal uniqueness criterion? - by bo198214 - 05/23/2008, 12:07 PM
Uniqueness of analytic tetration - by Kouznetsov - 09/30/2008, 07:58 AM
RE: Universal uniqueness criterion? - by bo198214 - 10/04/2008, 11:19 PM
RE: Universal uniqueness criterion? - by bo198214 - 06/19/2009, 02:51 PM
RE: miner error found in paper - by bo198214 - 06/19/2009, 04:53 PM
RE: Universal uniqueness criterion? - by bo198214 - 06/19/2009, 06:25 PM
RE: Universal uniqueness criterion? - by bo198214 - 06/19/2009, 07:59 PM
RE: Universal uniqueness criterion? - by bo198214 - 06/20/2009, 02:10 PM
RE: Universal uniqueness criterion? - by bo198214 - 07/05/2009, 06:54 PM

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