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Proof.
Consider the case z ≤ − 1 z\leq-1
(4.126) d ζ − ζ − = d r − r − + − 1 J d r − r − = − h d z + ϵ T − − 1 J h d z \frac{d\zeta_{-}}{\zeta_{-}}=\frac{dr_{-}}{r_{-}}+\sqrt{-1}J\frac{dr_{-}}{r_{-}}=-hdz+\epsilon_{T}-\sqrt{-1}Jhdz
The result then easily follows from the asymptotics of h h 4.16 ω ~ \tilde{\omega} 3.349