Dynamics of Linear Systems over Finite Commutative Rings
Rings and Algebras
2017-09-26 v1
Abstract
The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous publication, the last two authors developed an efficient algorithm to determine whether a linear dynamical system over a finite commutative ring is a fixed point system or not. The algorithm can also be used to reduce the problem of finding the cycles of such a system to the case where the system is given by an automorphism. Here, we further analyze the cycle structure of such a system and develop a method to determine its cycles.
Keywords
Cite
@article{arxiv.1709.08579,
title = {Dynamics of Linear Systems over Finite Commutative Rings},
author = {Yangjiang Wei and Guangwu Xu and Yi Ming Zou},
journal= {arXiv preprint arXiv:1709.08579},
year = {2017}
}