The iteration of cubic polynomials Part II: patterns and parapatterns
The iteration of cubic polynomials Part II: patterns and parapatterns
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DOI：
10.1007/bf02392761
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发表时间：
1992-12
期刊：
影响因子：
3.7
通讯作者：
Bodil Branner;J. Hubbard
中科院分区：
文献类型：
--
作者：
Bodil Branner;J. Hubbard
导言231 infinity.在文献[BH]中，我们证明了多项式ea，B（z）= Z3 - 3a 2 z + B的轨迹的拓扑，其中至少有一个临界点逃逸.在本文中，我们将描述该轨迹是如何被打破，根据是否一个或两个临界点逃脱。本文和前一篇文章对有一个临界点逃逸的三次多项式空间给出了完整的描述。这本身就很有趣，但也应该提供工具，让我们爬到立方连通性轨迹：没有临界点逃脱的轨迹。更具体地说，它应该允许我们用拉伸射线的形式给出这个轨迹的部分描述;这将是第三篇论文的目的。
INTRODUCTION 231 infinity. In the previous paper [BH], we identified the topology of the locus of polynomials ea, b (z)= Z 3-3a2z+ b where at least one critical point escapes. In this paper we will describe how that locus is broken up according to whether one or both critical points escape. This paper and the previous one give a complete description of the space of cubic polynomials for which one critical point escapes. This is of interest in itself, but should also provide tools for creeping up to the cubic connectedness locus: the locus where neither critical point escapes. More particularly, it should allow us to give a partial description of this locus in terms of stretching rays; this will be the object of the third paper.