对称立方层合
Symmetric Cubic Laminations
摘要：
为了研究$d$连通度轨迹，Thurston研究了单位圆上的$d$ -元组映射\emph{$σ_d$-invariant laminations}，并建立了二次多项式空间$f(z) = z^2 +c$的拓扑模型.本着Thurston的工作精神，我们在三篇系列文章中考虑所有\emph{cubic symmetric polynomials} $f_λ(z)=z^3+λ^2 z$的空间。本文是系列研究的第一篇，我们构造了一个叠层$C_sCL$和单位圆${\mathbb{S}}$的诱导因子空间${\mathbb{S}}/C_sCL$。正如将在该系列的第三篇论文中验证的那样，${\mathbb{S}}/C_sCL$是\emph{cubic symmetric connected locus}的单调模型，即具有连通Julia集的所有三次对称多项式的空间。
英文摘要：
To investigate the degree $d$ connectedness locus, Thur\-ston studied \emph{$σ_d$-invariant laminations}, where $σ_d$ is the $d$-tupling map on the unit circle, and built a topological model for the space of quadratic polynomials $f(z) = z^2 +c$. In the spirit of Thurston's work, we consider the space of all \emph{cubic symmetric polynomials} $f_λ(z)=z^3+λ^2 z$ in a series of three articles. In the present paper, the first in the series, we construct a lamination $C_sCL$ together with the induced factor space ${\mathbb{S}}/C_sCL$ of the unit circle ${\mathbb{S}}$. As will be verified in the third paper of the series, ${\mathbb{S}}/C_sCL$ is a monotone model of the \emph{cubic symmetric connected locus}, i.e. the space of all cubic symmetric polynomials with connected Julia sets.
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