partial invariant equations ?

[tommy1729]

Together with a friend (mick) i was wondering about the following.

Let g be an entire function.

Let A be a jordan curve on the riemann sphere going through the point oo.

Let g(A)=B be a similar curve that has no points in common with A. (so A is not free to choose !)

Let x be any element of A then we have

f(x) = f(g(x))

In particular for this forum ofcourse g(x) = exp(x).

regards

tommy1729