09/16/2011, 12:23 PM

a vague idea

let c be positive real , n positive integer and f(x) be the C^1 half-iterate of c + x^(2n).

let g(x) be the locally analytic half-iterate of c - x^(2n) expanded at the negative fixpoint.

choose c and n such that f(0) and g(0) = Q

can we choose c and n such that f(x) and g(x) are locally algebraicly related ?

i mean is there a polynomial P such that P(f(x),g(x),c,Q) = 0 ?

regards

tommy1729

let c be positive real , n positive integer and f(x) be the C^1 half-iterate of c + x^(2n).

let g(x) be the locally analytic half-iterate of c - x^(2n) expanded at the negative fixpoint.

choose c and n such that f(0) and g(0) = Q

can we choose c and n such that f(x) and g(x) are locally algebraicly related ?

i mean is there a polynomial P such that P(f(x),g(x),c,Q) = 0 ?

regards

tommy1729