Axiom A polynomial skew products of ℂ2 and their postcritical sets – ERRATUM
Axiom A polynomial skew products of ℂ2 and their postcritical sets – ERRATUM
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Axiom A ℂ2 的多项式偏斜积及其后临界集 – ERRATUM
DOI：
10.1017/s0143385710000568
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发表时间：
2010
影响因子：
0.9
通讯作者：
Suzanne Lynch Hruska
中科院分区：
文献类型：
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作者：
Laura Demarco;Suzanne Lynch Hruska
其中p和q是多项式。我们考虑了公理A的斜积，并将其全纯推广到P2的d ≥ 2次自同态.在文[DH]中，我们研究了C2的一个特殊子集中临界点的轨道，并构造了公理A映射的新例子。在那篇论文中，我们对多项式斜积做了一个错误的假设，这对我们的主要例子成立，但一般都失败了。在本文中，我们描述了错误并修正了我们主要结果的证明。我们还指出，没有这个额外的假设，原文中的哪些陈述不成立。我们要感谢角博树（Hiroki Sumi）提醒我们注意这个错误，并仔细描述了一个假设失败的例子（见[Su，备注4.13]）。我们也感谢中根静雄对原文的仔细阅读。
where p and q are polynomials. We consider skew products which are Axiom A and extend holomorphically to endomorphisms of P2 of degree d ≥ 2. In the article [DH], we studied orbits of critical points in a distinguished subset of C2, and we constructed new examples of Axiom A maps. In that paper we made an erroneous assumption about polynomial skew products, which holds for our main examples but fails in general. In this note, we describe the mistake and fix the proofs of our main results. We also indicate which statements in the original article do not hold without this extra assumption. We would like to thank Hiroki Sumi for bringing the mistake to our attention and carefully describing an example for which the assumption fails (see [Su, Remark 4.13]). We also thank Shizuo Nakane for his careful reading of the original article.