Julia sets of polynomials are uniformly perfect

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Let ƒ be a polynomial of degree at least two. We shall show that the Julia set J(ƒ) of ƒ is uniformly perfect. This means that there is a constant cϵ(0, 1) depending on ƒ only such that whenever zɛJ(f) and 0 < r < diam J(ƒ) then J(ƒ) intersects the annulus {w:cr ≤ w — z\ ≤r.

Original languageEnglish (US)
Pages (from-to)153-159
Number of pages7
JournalBulletin of the London Mathematical Society
Issue number2
StatePublished - Mar 1994

ASJC Scopus subject areas

  • General Mathematics


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