 The super of exp(z)(z^2 + 1) + z. - Printable Version +- Tetration Forum (https://math.eretrandre.org/tetrationforum) +-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) +--- Thread: The super of exp(z)(z^2 + 1) + z. (/showthread.php?tid=1073) The super of exp(z)(z^2 + 1) + z. - tommy1729 - 03/14/2016 Im very intrested in The super of exp(z)(z^2 + 1) + z. Notice it has only 2 fixpoints. Also The super of exp(z)(z^2 + 1) + z = L. Does it have solutions z for every L ? Why ? They determine the branch structure / singularities. Regards Tommy1729 RE: The super of exp(z)(z^2 + 1) + z. - tommy1729 - 03/15/2016 So we need to show f = exp(z) (1+x^2) + z is surjective to the complex plane. F maps [- oo , oo ] to [- oo , oo ]. Also conj(f(z)) = f(conj(z)). Hence f is surjective on the reals. By picard if f(z) =\= L then this L is unique. But by the above f(conj(z)) =\= conj L. Hence contradicting picard. Therefore f is surjective to the complex plane. So the singularities of its super are bounded. Q.E.D. Regards Tommy1729