Toshiyuki SUGAWA
An explicit bound for uniform perfectness of the Julia sets of rational maps
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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