与复动力系统相关的C* 代数和倒向轨道结构
C*-algebras associated with complex dynamical systems and backward orbit structure
摘要：
设$R$是一个有理函数。$R$的迭代$(R^n)_n$给出了黎曼球面上的复动力系统。通过关联一个$C^*$ -代数，研究了该$C^*$ -代数与原复动力系统之间的关系.在这个简短的说明中，我们恢复的$n$次向后轨道的数量计数没有重数开始于分支点在相关的$C^*$ -代数规范作用。特别地，我们可以部分地想象在$R$的迭代下，一个分支点是如何移动到另一个分支点的。我们使用KMS态和Perron-Frobenius型算子的空间的轨迹来显示它。
英文摘要：
Let $R$ be a rational function. The iterations $(R^n)_n$ of $R$ gives a complex dynamical system on the Riemann sphere. We associate a $C^*$-algebra and study a relation between the $C^*$-algebra and the original complex dynamical system. In this short note, we recover the number of $n$-th backward orbits counted without multiplicity starting at branched points in terms of associated $C^*$-algebras with gauge actions. In particular, we can partially imagine how a branched point is moved to another branched point under the iteration of $R$. We use KMS states and a Perron-Frobenius type operator on the space of traces to show it.
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