Polynomial maps with a Julia set of positive measure
Polynomial maps with a Julia set of positive measure
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发表时间：
1994-02
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通讯作者：
T. Nowicki;S. Strien
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作者：
T. Nowicki;S. Strien
本文证明了存在L_0，使得对任意偶数L >= L_0，存在c_1\in \rz$，使得z --> z^L + c_1$的Julia集具有正的Lebesgue测度.这解决了一个老问题。编者按：1997年，泽维尔·布夫（Xavier Buff）指出，这个论证存在严重缺陷，在证明中留下了一个空白。目前（1999年），多项式的问题与一个积极的措施朱莉娅集仍然开放。
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.