Institute for Mathematical Sciences

Preprint ims94-3

T. Nowicki and S. van Strien
Polynomial Maps with a Julia Set of Positive Measure

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.

View ims94-3 (PDF format)