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Julia sets of rational functions are uniformly perfect

Published online by Cambridge University Press:  24 October 2008

A. Hinkkanen
A. Hinkkanen
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, U.S.A.
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Abstract

Let f be a rational function of degree at least two. We shall prove that the Julia set J(f) of f is 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 .

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 113 , Issue 3 , May 1993 , pp. 543 - 559
Copyright
Copyright © Cambridge Philosophical Society 1993

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