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Polynomial maps with a Julia set of positive measure

Tomasz Nowicki·Sebastian van Strien
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Abstract

In this paper we shall show that there exists L_0 such that for each even integer L >= L_0 there exists $c_1 \in \rz$ for which the Julia set of $z --> z^L + c_1$ has positive Lebesgue measure. This solves an old problem. Editor's note: In 1997, it was shown by Xavier Buff that there was a serious flaw in the argument, leaving a gap in the proof. Currently (1999), the question of polynomials with a positive measure Julia sets remains open.

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Tomasz Nowicki, Sebastian van Strien. 1994-02-16. Polynomial maps with a Julia set of positive measure. https://arxiv.org/abs/math/9402215

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