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Bulletin of the London Mathematical Society 1994 26(2):153-159; doi:10.1112/blms/26.2.153
© 1994 by London Mathematical Society
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© London Mathematical Society

Julia Sets of Polynomials are Uniformly Perfect

A. Hinkkanen

Department of Mathematics, University of Illinois at Urbana-Champaign Urbana, IL 61801, USA

Received 12 February 1992. Revision received 8 October 1992.

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


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