Green’s function and anti-holomorphic dynamics on a torus

Bergweiler, Walter; Eremenko, Alexandre

doi:10.1090/proc/13044

Green’s function and anti-holomorphic dynamics on a torus
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Proc. Amer. Math. Soc. 144 (2016), 2911-2922 Request permission

Abstract:

We give a new, simple proof of the fact recently discovered by C.-S. Lin and C.-L. Wang that the Green function of a torus has either three or five critical points, depending on the modulus of the torus. The proof uses anti-holomorphic dynamics. As a byproduct we find a one-parametric family of anti-holomorphic dynamical systems for which the parameter space consists only of hyperbolic components and analytic curves separating them.

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