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 conjecture 2 fixpoints tommy1729 Ultimate Fellow Posts: 1,370 Threads: 335 Joined: Feb 2009 08/11/2010, 10:07 PM a conjecture about 2 fixpoints. it was once asked when 2 fixpoint based real iterates coincide. perhaps an example. conjecture 2 fixpoints : let f(z) be a laurent series meromorphic everywhere apart in circle D with center at origin and radius 1/a. f(z) is not periodic. f(-z) = -f(z) f(z) has only 2 fixpoints. those fixpoints are -1,+1. f ' (-1) = -1/a <=> f ' (1) = 1/a and a > 1. if lim n-> oo a^n (f^[n](z) - f[2n](z)) exists and is meromorphic on C\D then this is the superfunction matching both fixpoints. regards 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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