Siegel有理映射的组合动力学性质
Dynamics of Siegel Rational Maps with Prescribed Combinatorics
摘要：
本文将Thurston关于后临界有限有理映射的组合判据推广到一类具有有界Siegel圆盘的有理映射。这类Siegel有理映射的组合刻画在一般Siegel有理映射的研究中发挥着特殊的作用。作为应用之一，我们证明了对于任何具有有界型Siegel圆盘的二次有理映射，Siegel圆盘的边界是通过其中一个或两个临界点的拟圆.
英文摘要：
We extend Thurston's combinatorial criterion for postcritically finite rational maps to a class of rational maps with bounded type Siegel disks. The combinatorial characterization of this class of Siegel rational maps plays a special role in the study of general Siegel rational maps. As one of the applications, we prove that for any quadratic rational map with a bounded type Siegel disk, the boundary of the Siegel disk is a quasi-circle which passes through one or both of the critical points.
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