论文标题
台球系统及其应用于信息理论熵
A System of Billiard and Its Application to Information-Theoretic Entropy
论文作者
论文摘要
在本文中，我们根据图的ihara zeta函数定义了一个称为ihara熵的信息理论熵。动态系统由台球球和一组反射器组成，对应于组合图。反射器由图的顶点表示。台球在两个反射器之间的运动由边缘表示。该图的主要周期生成了相应符号动力学系统的双限序列。给定长度的不同原始循环的数量可以用定向线图的邻接矩阵表示。它还构建了Ihara Zeta功能的正式功率系列扩展。因此，Ihara熵与台球动态系统有着深厚的联系。作为一种信息理论熵，它履行了广义的香农 - 金钦公理。这是一个弱分解的熵，其构图法由《拉扎德》正式集体法给出。
In this article, we define an information-theoretic entropy based on the Ihara zeta function of a graph which is called the Ihara entropy. A dynamical system consists of a billiard ball and a set of reflectors correspond to a combinatorial graph. The reflectors are represented by the vertices of the graph. Movement of the billiard ball between two reflectors is represented by the edges. The prime cycles of this graph generate the bi-infinite sequences of the corresponding symbolic dynamical system. The number of different prime cycles of a given length can be expressed in terms of the adjacency matrix of the oriented line graph. It also constructs the formal power series expansion of Ihara zeta function. Therefore, the Ihara entropy has a deep connection with the dynamical system of billiards. As an information-theoretic entropy, it fulfils the generalized Shannon-Khinchin axioms. It is a weakly decomposable entropy whose composition law is given by the Lazard formal group law.
