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