Algorithmic aspects of branched coverings IV/V. Expanding maps
Algorithmic aspects of branched coverings IV/V. Expanding maps
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DOI：
10.1090/tran/7199
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发表时间：
2016-10
影响因子：
1.3
通讯作者：
L. Bartholdi;Dzmitry Dudko
中科院分区：
文献类型：
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作者：
L. Bartholdi;Dzmitry Dudko
瑟斯顿映射是临界点有有限正向轨道的球面的分支自覆盖。我们给出了Thurston映射的组合和代数表征，这些映射是与展开映射相同的“无列维”映射和具有“收缩二集”的映射。我们证明了每个Thurston映射沿着唯一的最小多重曲线分解成无levy和有限阶的碎片，并且这种分解是可算法计算的。每一件作品都有一个几何结构。我们将这些结果应用于后临界有限多项式的配对，扩展了Mary Rees和Tan Lei的一个准则：当且仅当它们不允许周期射线的循环时，它们正在展开。
Thurston maps are branched self-coverings of the sphere whose critical points have finite forward orbits. We give combinatorial and algebraic characterizations of Thurston maps that are isotopic to expanding maps as "Levy-free" maps and as maps with "contracting biset". We prove that every Thurston map decomposes along a unique minimal multicurve into Levy-free and finite-order pieces, and this decomposition is algorithmically computable. Each of these pieces admits a geometric structure. We apply these results to matings of post-critically finite polynomials, extending a criterion by Mary Rees and Tan Lei: they are expanding if and only if they do not admit a cycle of periodic rays.