有限组合秩动力系统的狄利克雷级数
Dirichlet series for finite combinatorial rank dynamics
摘要：
我们引入一类群自同态-那些有限的组合秩-表现出缓慢的轨道增长。利用相应的狄利克雷级数得到了一个精确的轨道计数公式，并证明了在连通情形下该级数具有闭的有理形式.狄利克雷级数的分析性质与轨道增长渐近性有关：根据收敛横坐标的位置和极点的程度，可以找到各种轨道增长渐近性，所有这些都是多项式有界的。
英文摘要：
We introduce a class of group endomorphisms -- those of finite combinatorial rank -- exhibiting slow orbit growth. An associated Dirichlet series is used to obtain an exact orbit counting formula, and in the connected case this series is shown to have a closed rational form. Analytic properties of the Dirichlet series are related to orbit-growth asymptotics: depending on the location of the abscissa of convergence and the degree of the pole there, various orbit-growth asymptotics are found, all of which are polynomially bounded.
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