Linear Dynamical System over Finite Distributive Lattice  

作　　者：DENG Aiping GONG Xiaoyue MA Hongcai 邓爱平;弓晓月;马红彩(College of Science, Donghua University, Shanghai 201620, China)

机构地区：[1]College of Science, Donghua University, Shanghai 201620, China

出　　处：《Journal of Donghua University(English Edition)》2021年第3期264-271,共8页东华大学学报（英文版）

基　　金：National Natural Science Foundation of China(Nos.11671258 and 11371086)。

摘　　要：A finite dynamical system(FDS)over a lattice L is a pair(S(L),f),where S(L)is a left-L module and f is a mapping from S into itself.The phase space of(S(L),f)is a digraph whose vertex set is S(L)and there is an arc from x to y if y=f(x).Let L be a finite distributive lattice,A an n×n matrix over L,and f(x)=Ax.The structure of the phase space of the FDS(Ln,f)is discussed.The number of limit cycles in the phase space of(Ln,f)is described in Möbius function.The phase spaces of some invertible,nilpotent,and idempotent FDS(Ln,f)are characterized explicitly.

关 键 词：finite distributive lattice linear dynamical system phase space limit cycle rooted in-tree 

分 类 号：O159[理学—数学]