Rational functions with real multipliers
classification
🧮 math.DS
math.CV
keywords
belongscirclerationalfunctionfunctionsjuliamultipliersreal
read the original abstract
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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