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

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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.
6 pages

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Complex Variables, Dynamical Systems, 37F10, 30D05, 30D30

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http://salesiana.dossiersoluciones.com/handle/123456789/226847

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0808.3800
 http://arxiv.org/abs/0808.3800
 Proc. Amer. Math. Soc. 137 (2009), 2329-2333
 doi:10.1090/S0002-9939-08-09788-8

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arXiv