扩张Thurston映射的完美拟合无限链
Infinite chains of perfect fits for expanding Thurston maps
浏览论文内容
中文总结 AI 辅助
该研究证明多项式配对中完美拟合无限链不存在的结论是全纯现象，构造了含周期临界轨道的组合扩张Thurston映射，其层叠结构存在无限多完美拟合无限链，且无法由扩张有理映射实现。
中文摘要 AI 辅助
具有树状Julia集的两个后临界有限多项式的拓扑配对由一对圆层叠结构Λ±编码，其坍缩会生成一条充满球面的曲线。当Λ+的一片叶与Λ-的一片叶共享一个端点时，它们就形成了一个完美拟合。Petersen和Meyer记录的Epstein未发表命题表明，对于诚实的d次多项式的配对，无限直径的射线等价类（即完美拟合的无限链）是不可能存在的。我们证明这种有限性是一种真正的全纯现象。通过允许动力学承载周期临界轨道，我们构造了组合扩张Thurston映射（其无法由任何扩张有理映射实现），这类映射虽允许不变充满球面的曲线，但其层叠结构Λ±包含完美拟合的无限链，实际上是无限多个这样的链。
英文摘要
The topological mating of two postcritically finite polynomials with dendritic Julia sets is encoded by a pair of circle laminations $Λ^{\pm}$, whose collapse produces a sphere-filling curve. When a leaf of $Λ^{+}$ and a leaf of $Λ^{-}$ share an endpoint they form a perfect fit. An unpublished proposition of Epstein, recorded by Petersen and Meyer, shows that for matings of honest degree-$d$ polynomials an infinite-diameter ray equivalence class, i.e. an infinite chain of perfect fits is impossible. We show that this finiteness is a genuinely holomorphic phenomenon. Allowing the dynamics to carry a periodic critical orbit, we construct combinatorially expanding Thurston maps-realized by no expanding rational map-that admit invariant sphere-filling curves yet whose laminations $Λ^{\pm}$ contain infinite chains of perfect fits, in fact infinitely many of them.
发表机构
- University of Chicago（芝加哥大学）
机构由 AI 辅助整理，请以论文原文为准。
