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Universal uniqueness criterion?
#31
Theorem.
Let be a function that is biholomorphic on both of the initial regions and that share as boundaries the same conjugate pair of fixed points of f. Also let f have no other fixed points. Let there be two Abel functions of f, and , that are biholomorphic on these initial regions and satisfy A(d) = c.
For each f, there exists exactly one biholomorphism on a single simply connected open set such that (i is an index that can be 1 or 2) i.e. there is an analytic continuation, and it's unique.

Proof.
1.
Let be disjoint, simply connected domains that have as boundaries:
(1) , disjoint curves which are homeomorphic to (0,1);
(2) and , which are boundaries of, but not contained in, .

2.
Let be a biholomorphism on , where , (tried to make the domain of biholomorphism into an open set) that:
(1) bijects to ;
(2) has a conjugate pair of fixed points and ;
(3) has no other fixed points in the domain of biholomorphy.

3.
(1) Let , a biholomorphism on , and , a biholomorphism on , both satisfy for all applicable z. (for all z such that A(f(z)) is defined)
(2) Let for some .

to be continued
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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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