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 conjecture 2 fixpoints tommy1729 Ultimate Fellow Posts: 1,370 Threads: 335 Joined: Feb 2009 08/12/2010, 07:12 PM (This post was last modified: 08/12/2010, 07:32 PM by tommy1729.) im beginning to doubt ... the symmetry seems very wrong. if f(z) = f(-z) or -f(-z) then how are the fixpoints symmetric ??? i think only the following makes sense : (up to a linear transform ) for a nonperiodic entire function with only attractive fixpoints : superfunction = lim n-> oo (f^(n)[z] - f^(2n)[z])/D f^(n)[z] and using l'hospital rule if necc. the 'D' stands for derivate and perhaps this might not work and will need to be replaced by f ' [f^(3n)[z]] ^n. one of the assumptions is lim n -> oo D f^(n)[z] = O ( f ' [f^(3n)[z]] ^n ) but im not sure about that. if the superfunctions as defined above maps C to C/(const) that would be intresting ; they are candidates for being entire superfunctions consistant with all fixpoints. we might be able to plug in a periodic theta function to get rid of our problems ... but the problem with that is that a small variation might lead f^(n)[z + theta(z)] to go to another fixpoint and thus causing havoc. however not necc for all f(z) and all theta(z) , there is still hope for a theta. i might remove the other posts in this thread later ... tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread conjecture 2 fixpoints - by tommy1729 - 08/11/2010, 10:07 PM RE: conjecture 2 fixpoints - by tommy1729 - 08/12/2010, 12:16 PM RE: conjecture 2 fixpoints - by tommy1729 - 08/12/2010, 07:12 PM RE: conjecture 2 fixpoints - by tommy1729 - 08/15/2010, 07:08 PM

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