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arXiv · 0808.3800

Meromorphic functions with linearly distributed values and Julia sets of rational functions

Walter Bergweiler·Alexandre Eremenko
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Abstract

If the preimage of a four-point set under a meromorphic function belongs to the real line, then the image of the real line is contained in a circle in the Riemann sphere. We include an application of this result to holomorphic dynamics: if the Julia set of a rational function is contained in a smooth curve then it is contained in a circle.

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Walter Bergweiler, Alexandre Eremenko. 2008-08-27. Meromorphic functions with linearly distributed values and Julia sets of rational functions. https://doi.org/10.1090/s0002-9939-08-09788-8

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