论文标题
有限细分规则的征税和瑟斯顿障碍
Levy and Thurston obstructions of finite subdivision rules
论文作者
论文摘要
对于有限细分规则的细分映射球的批判后有限的分支覆盖物，我们定义了非扩展的刺，这些棘突确定了在非避免半决赛中征收循环的存在。尤其是当有限细分规则具有边缘细分的多项式生长时，该算法终止很快，并且征税周期的存在等同于存在瑟斯顿障碍物。为了显示征税和瑟斯顿障碍物之间的等效性，我们通过朝圣和棕褐色与图形相交的障碍物定理相交的弧线概括了障碍物定理。作为推论，我们证明，对于一对批判性有限的多项式，如果至少一个多项式的核心熵为零，那么当且仅当交配具有瑟斯顿障碍时，他们的交配就具有征费循环。
For a post-critically finite branched covering of the sphere that is a subdivision map of a finite subdivision rule, we define non-expanding spines which determine the existence of a Levy cycle in a non-exhaustive semi-decidable algorithm. Especially when a finite subdivision rule has polynomial growth of edge subdivisions, the algorithm terminates very quickly, and the existence of a Levy cycle is equivalent to the existence of a Thurston obstruction. In order to show the equivalence between Levy and Thurston obstructions, we generalize the arcs intersecting obstruction theorem by Pilgrim and Tan to a graph intersecting obstruction theorem. As a corollary, we prove that for a pair of post-critically finite polynomials, if at least one polynomial has core entropy zero, then their mating has a Levy cycle if and only if the mating has a Thurston obstruction.
