三次临界像与带游动间隙的多项式
Cubic Critical Portraits and Polynomials with Wandering Gaps
摘要：
Thurston引入了$\si_d$ -不变的叠层（其中$\si_d(z)$与$z^d:\ucirc\to \ucirc$，$d\ge 2$重合），并将\emph{wandering $k$-gons}定义为集合$\T\subset \ucirc$，使得$\si_d^n(\T)$由所有$n\ge 0$的$k\ge 3$不同点组成，并且平面中所有集合$\si_d^n(\T)$的凸包是成对不相交的.他证明了$\si_2$没有游荡的$k$ -簇。将$k$ -\emph{WT-lamination}漂移的层压称为\emph{WT-lamination}。在最近的一篇论文中，它表明，不可数许多三次WT-叠层，与成对的非共轭诱导映射在相应的商空间$J$，可实现为三次多项式在其（局部连通）的朱莉娅集。在本文中，我们使用一种新的方法来构造具有所有上述性质的三次WT-叠层和额外的性质，即相应的游荡分支点的$J$有一个密集的轨道在每个子弧的$J$（我们称之为轨道\emph{condense}），并显示，临界画像对应于这样的叠层是不可数密集的空间$\A_3$的所有三次临界画像。
英文摘要：
Thurston introduced $\si_d$-invariant laminations (where $\si_d(z)$ coincides with $z^d:\ucirc\to \ucirc$, $d\ge 2$) and defined \emph{wandering $k$-gons} as sets $\T\subset \ucirc$ such that $\si_d^n(\T)$ consists of $k\ge 3$ distinct points for all $n\ge 0$ and the convex hulls of all the sets $\si_d^n(\T)$ in the plane are pairwise disjoint. He proved that $\si_2$ has no wandering $k$-gons. Call a lamination with wandering $k$-gons a \emph{WT-lamination}. In a recent paper it was shown that uncountably many cubic WT-laminations, with pairwise non-conjugate induced maps on the corresponding quotient spaces $J$, are realizable as cubic polynomials on their (locally connected) Julia sets. In the present paper we use a new approach to construct cubic WT-laminations with all of the above properties and the extra property that the corresponding wandering branch point of $J$ has a dense orbit in each subarc of $J$ (we call such orbits \emph{condense}), and to show that critical portraits corresponding to such laminations are uncountably dense in the space $\A_3$ of all cubic critical portraits.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
