Julia sets of rational functions are uniformly perfect

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Let f be a rational function of degree at least two. We shall prove that the Julia set J(f) of fis uniformly perfect. This means that there is a constant c∊(0,1)depending on f only such that whenever z∊J(f) and 0 < r < diam J(f) then J(f) intersects the annulus {w: cr≤| w — z|≤r}.

Original languageEnglish (US)
Pages (from-to)543-559
Number of pages17
JournalMathematical Proceedings of the Cambridge Philosophical Society
Issue number3
StatePublished - May 1993

ASJC Scopus subject areas

  • General Mathematics


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