亚纯函数的后奇异动力学
Prescribing the Postsingular Dynamics of Meromorphic Functions
摘要：
我们证明了任意离散平面序列$S$上的动力学都可以由某个超越亚纯函数的后奇异动力学实现，只要我们允许$S$的小扰动.这项工作的影响，类似的结果DeMarco，科赫和McMullen有限$S$在合理的设置。证明包含了一种方法，用于构造亚纯函数具有良好的控制，在这两个后奇异集的$f$和几何的$f$，使用折叠定理的主教和经典的不动点定理的吉洪诺夫。
英文摘要：
We show that any dynamics on any discrete planar sequence $S$ can be realized by the postsingular dynamics of some transcendental meromorphic function, provided we allow for small perturbations of $S$. This work was influenced by an analogous result of DeMarco, Koch and McMullen for finite $S$ in the rational setting. The proof contains a method for constructing meromorphic functions with good control over both the postsingular set of $f$ and the geometry of $f$, using the Folding Theorem of Bishop and a classical fixpoint theorem of Tychonoff.
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