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

Walter Bergweiler; Alexandre Eremenko

doi:10.1090/proc/13044

journal article Mar 16, 2016

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

Walter Bergweiler Alexandre Eremenko

Proceedings of the American Mathematical Society Vol. 144 No. 7 pp. 2911-2922 · American Mathematical Society (AMS)

View at Publisher Save 10.1090/proc/13044

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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Citations

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References

Details

Published: Mar 16, 2016
Vol/Issue: 144(7)
Pages: 2911-2922
License: View

Authors

Funding

National Science Foundation Award: DMS-1361836

Cite This Article

Walter Bergweiler, Alexandre Eremenko (2016). Green’s function and anti-holomorphic dynamics on a torus. Proceedings of the American Mathematical Society, 144(7), 2911-2922. https://doi.org/10.1090/proc/13044

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

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