Tan Lei and Shishikura's example of non-mateable degree 3 polynomials without a Levy cycle
Tan Lei and Shishikura's example of non-mateable degree 3 polynomials without a Levy cycle
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Tan Lei 和 Shishikura 的无 Levy 环的不可配合 3 次多项式的示例
DOI：
10.5802/afst.1358
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Arnaud Ch'eritat
中科院分区：
文献类型：
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作者：
Arnaud Ch'eritat
在介绍了所谓的慢多项式匹配过程，并提出了一个将它与其他多项式匹配概念联系起来的猜想之后，我们展示了由Shishikura和Tan Lei提出的两次3次后临界有限多项式的慢匹配的共形正确图像，作为一个没有Levy圈的非匹配多项式对的例子。这些图片显示了Julia集的极限，这似乎与6次有理映射的Julia集有关。我们用捏缩球的形式对此给出了猜想解释，并给出了进一步的共形表示。
After giving an introduction to the procedure dubbed slow polynomial mating and stating a conjecture relating this to other notions of polynomial mating, we show conformally correct pictures of the slow mating of two degree 3 post critically finite polynomials introduced by Shishikura and Tan Lei as an example of a non matable pair of polynomials without a Levy cycle. The pictures show a limit for the Julia sets, which seems to be related to the Julia set of a degree 6 rational map. We give a conjectural interpretation of this in terms of pinched spheres and show further conformal representations.