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2008•Proceedings of the American Mathematical SocietyOpen access

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

Walter Bergweiler, Alexandre Erëmenko

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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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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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Available 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.

Key concepts: Meromorphic function, Julia set, Riemann sphere, Holomorphic function, Mathematics, Rational function, Line (geometry), Pure mathematics

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