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

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.

6 pages

References in corpus (1)

• Rational functions with real multipliers

Cited by in corpus (7)

• Extremality and dynamically defined measures, part II: Measures from conformal dynamical systems
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• Dimension rigidity in conformal structures
• Reduced dynamical systems
• Rigidity and absence of line fields for meromorphic and Ahlfors islands maps
• Second order linear differential equations with a basis of solutions having only real zeros
• Rational functions with real multipliers