Institute for Mathematical Sciences

Preprint ims98-1a

S. Zakeri
Biaccessiblility in Quadratic Julia Sets I: The Locally-Connected Case

Abstract: Let $f:z\mapsto z^2+c$ be a quadratic polynomial whose Julia set $J$ is locally-connected. We prove that the Brolin measure of the set of biaccessible points in $J$ is zero except when $f(z)=z^2-2$ is the Chebyshev quadratic polynomial for which the corresponding measure is one.
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