Polynomial maps with a Julia set of positive measure
Tomasz Nowicki, Sebastian van Strien
Abstract
In this paper we shall show that there exists L0 such that for each even integer L >= L0 there exists c1 ∈ for which the Julia set of z --> zL + c1 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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