Toshiyuki SUGAWA

Abstract

A compact set \$ C \$ in the Riemann sphere is called uniformly perfect if the moduli of annuli separating \$ C \$ are bounded. Ma\~n\'e-da Rocha and Hinkkanen showed independently the uniform perfectness of the Julia sets of rational maps of degree \$ \ge 2, \$ but they presented no explicit bounds for uniform perfectness. In this note, we shall provide such an explicit bound and, as a result, we give another proof of uniform perfectness of the Julia sets. As an application, we refer to a lower estimate of the Hausdorff dimension of the Julia sets.

submission: August 4, 1997
revision: August 7, 1998

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