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+--- 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