论文标题
用于立方对称多项式的熔岩算法
Lavaurs algorithm for cubic symmetric polynomials
论文作者
论文摘要
为了调查$ d $连接的基因座，瑟斯顿研究了\ emph {$σ_d$ -invariant laminations}，其中$σ_d$是单位圈子上的$ d $ -tupling地图，并为Quadratic polynomials $ f_c（z）$ f_c（z）= z^2 +c $构建了拓扑模型。本着同样的精神，我们考虑了三篇文章中所有\ emph {立方对称多项式} $f_λ（z）= z^3+λ^2 z $。在第一个中，我们将层压$ c_scl $与诱导因子空间$ \ mathbb {s}/c_scl $一起构建，单位圆$ \ mathbb {s} $。正如将在第三篇论文中验证的那样，$ \ mathbb {s}/c_scl $是\ emph {立方对称性连接locus}的单调模型，即，所有立方对称性多种物质的空间与连接的Julia sets。在本文的本文中，我们开发了一种算法，用于构建类似于熔岩算法的$ c_scl $，用于构建组合模型$ \ MATHCAL {M}^{M}^{m comb} _2 _2 _2 $的mandelbrot set $ \ mathcal set $ \ nathcal {m} m} _2 $。
To investigate the degree $d$ connectedness locus, Thurston 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 $f_c(z) = z^2 +c$. In the same spirit, we consider the space of all \emph{cubic symmetric polynomials} $f_λ(z)=z^3+λ^2 z$ in three articles. In the first one we construct the 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, $\mathbb{S}/C_sCL$ is a monotone model of the \emph{cubic symmetric connectedness locus}, i.e., the space of all cubic symmetric polynomials with connected Julia sets. In the present paper, the second in the series, we develop an algorithm for constructing $C_sCL$ analogous to the Lavaurs algorithm for constructing a combinatorial model $\mathcal{M}^{comb}_2$ of the Mandelbrot set $\mathcal{M}_2$.
