## 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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