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
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