TY - JOUR

T1 - Julia sets of rational functions are uniformly perfect

AU - Hinkkanen, A.

N1 - Funding Information:
The author would like to thank the referee for his comments, and, in particular, for suggesting that Corollary 1 should be formulated and for correcting an error in Section 4-1. The author's research is partially supported by the Alfred P.Sloan Foundation and the U.S. National Science Foundation.

PY - 1993/5

Y1 - 1993/5

N2 - 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}.

AB - 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}.

UR - http://www.scopus.com/inward/record.url?scp=84971113358&partnerID=8YFLogxK

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U2 - 10.1017/S0305004100076192

DO - 10.1017/S0305004100076192

M3 - Article

AN - SCOPUS:84971113358

VL - 113

SP - 543

EP - 559

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 3

ER -