Thurston equivalence for rational maps with clusters
Thurston equivalence for rational maps with clusters
复制标题
具有簇的有理映射的瑟斯顿等价
DOI：
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发表时间：
2011
影响因子：
0.9
通讯作者：
Thomas Sharland
中科院分区：
文献类型：
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作者：
Thomas Sharland
摘要：我们研究具有第一周期和第二周期簇循环的有理图。给定簇的定义，我们表明，在度为 $d$ 且簇固定的情况下，有理映射的 Thurston 类由组合旋转数 $ 固定
ho$和簇周期的临界位移$delta$。在有理图是二次且具有二周期簇循环的情况下也将证明相同的结果，并且我们还将证明该陈述在更高次的情况下不再成立。
Abstract We investigate rational maps with period-one and period-two cluster cycles. Given the definition of a cluster, we show that, in the case where the degree is $d$ and the cluster is fixed, the Thurston class of a rational map is fixed by the combinatorial rotation number $
ho $ and the critical displacement $delta $of the cluster cycle. The same result will also be proved in the case where the rational map is quadratic and has a period-two cluster cycle, and we will also show that the statement is no longer true in the higher-degree case.