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


Authors: Walter Bergweiler and Alexandre Eremenko
Journal: Proc. Amer. Math. Soc. 144 (2016), 2911-2922
MSC (2010): Primary 31A05, 33E05, 37F10
DOI: https://doi.org/10.1090/proc/13044
Published electronically: March 16, 2016
MathSciNet review: 3487224
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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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Additional Information

Walter Bergweiler
Affiliation: Mathematisches Seminar, Christian–Albrecht–Universität zu Kiel, Ludewig–Meyn–Straße 4, 24098 Kiel, Germany
Email: bergweiler@math.uni-kiel.de

Alexandre Eremenko
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email: eremenko@math.purdue.edu

DOI: https://doi.org/10.1090/proc/13044
Received by editor(s): July 7, 2015
Published electronically: March 16, 2016
Additional Notes: The second author was supported by NSF grant DMS-1361836.
Communicated by: Svitlana Mayboroda
Article copyright: © Copyright 2016 American Mathematical Society