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 Mizugadro, pentation, Book MphLee Fellow Posts: 95 Threads: 7 Joined: May 2013 02/10/2015, 12:48 PM (This post was last modified: 02/10/2015, 12:49 PM by MphLee.) (02/09/2015, 10:35 PM)tommy1729 Wrote: For instance the solutions for bases between 1 and eta are unique. So basicly these are traditional fixpoint methods. I recently wrote about parabolic fixpoints and I assume your aware of the koenigs function. Truncating Taylor series by polynomials or other functions can lead to alternative ways of computation. mmhh... to be honest I don't know what is the Koenigs function. My knowledge is almost negative in this field (or immaginary xd). BTW I'm reading about it right now.. It actually says that if $f$ is a function with some properties (holomorphic mapping of the unit disck to itself... and so on) then there exist an unique holomorphic solution to the schroeder's equation $S(f(x))=f'(0)\cdot S(x)$ with $S(0)=0$ and $S'(0)=1$. Then this unique solution is called Koenigs function. So if the conditions of the Koenings theorem are satisfied by some function we are interested in it should give us an unique holomorphic solution to a schroeder equation, and since its conjugated with the abel equation we will get an unique Abel function as well... is this the point? When I have time I'll check the post you are talking about (parabolic fixedpoints) MathStackExchange account:MphLee « Next Oldest | Next Newest »