Renormalizations and Wandering Jordan Curves of Rational Maps
Renormalizations and Wandering Jordan Curves of Rational Maps
复制标题
有理映射的重整化和徘徊乔丹曲线
DOI：
10.1007/s00220-016-2623-x
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发表时间：
2016
影响因子：
2.4
通讯作者：
Lei Tan
中科院分区：
文献类型：
--
作者：
Guizhen Cui;Wenjuan Peng;Lei Tan
我们实现了一个允许组合分解的后临界有限有理映射的动态分解。我们把黎曼球分成两个完全不变的子集。一类是Julia集合的子集，该集合由无数个Jordan曲线组成。大多数人都在流浪。另一个由有限多个重整化的回调组成，可能还有无数个点。分解块上的商作用由枝晶动力系统编码。我们还介绍了一种外科手术程序，以产生具有徘徊约旦曲线和规定重整化的后临界有限理性映射。
We realize a dynamical decomposition for a post-critically finite rational map which admits a combinatorial decomposition. We split the Riemann sphere into two completely invariant subsets. One is a subset of the Julia set consisting of uncountably many Jordan curve components. Most of them are wandering. The other consists of components that are pullbacks of finitely many renormalizations, together with possibly uncountably many points. The quotient action on the decomposed pieces is encoded by a dendrite dynamical system. We also introduce a surgery procedure to produce post-critically finite rational maps with wandering Jordan curves and prescribed renormalizations.