由图的组合生成的符号动力学
Symbolic Dynamics Generated by a Combination of Graphs
摘要：
本文用一种精确的解析方法研究了图中所有可能路的数目随其长度的增长率。除了典型的增长率，即指数或多项式，我们确定了拉伸指数型增长的条件。这可以通过在相同的字母表上组合两个或更多个图来实现，以便获得由三角形映射生成的离散动力系统，其也可以被解释为离散非自治系统。由于图的顶点和边通常用于描述离散动力系统的状态和状态之间的转换，因此两个（或多个）图的组合可以被解释为一个系统对另一个系统的驱动或扰动。
英文摘要：
In this paper we investigate the growth rate of the number of all possible paths in graphs with respect to their length in an exact analytical way. Apart from the typical rates of growth, i.e. exponential or polynomial, we identify conditions for a stretched exponential type of growth. This is made possible by combining two or more graphs over the same alphabet, in order to obtain a discrete dynamical system generated by a triangular map, which can also be interpreted as a discrete non-autonomous system. Since the vertices and the edges of a graph usually are used to depict the states and transitions between states of a discrete dynamical system, the combination of two (or more) graphs can be interpreted as the driving, or perturbation, of one system by another.
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