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arxiv: 0810.2260 · v1 · pith:RQAN24KQnew · submitted 2008-10-13 · 🧮 math.DS · math.CV

Rational functions with real multipliers

classification 🧮 math.DS math.CV
keywords belongscirclerationalfunctionfunctionsjuliamultipliersreal
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Let f be a rational function such that the multipliers of all repelling periodic points are real. We prove that the Julia set of such a function belongs to a circle. Combining this with a result of Fatou we conclude that whenever J(f) belongs to a smooth curve, it also belongs to a circle. Then we discuss rational functions whose Julia sets belong to a circle.

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