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- Title
Linear dynamical systems of dimension two over the ring of integers modulo pt.
- Authors
Wei, Yangjiang; Xu, Heyan; Liang, Linhua
- Abstract
In this paper, we investigate the linear dynamical system f : ℤ p t 2 → ℤ p t 2 , where ℤ p t is the ring of integers modulo p t (p is a prime). In order to facilitate the visualization of this system, we associate a graph Γ (A) on it, whose nodes are the points of ℤ p t 2 , and for which there is an arrow from α to β , when α A = β for a fixed 2 × 2 matrix A. In this paper, the in-degree of each node in Γ (A) is obtained, and a complete description of Γ (A) is given, when A is an idempotent matrix, or a nilpotent matrix, or a diagonal matrix. The results in this paper generalize Elspas' [1959] and Toledo's [2005].
- Subjects
TOLEDO (Ohio); LINEAR dynamical systems; RINGS of integers; DIMENSION theory (Algebra)
- Publication
Discrete Mathematics, Algorithms & Applications, 2020, Vol 12, Issue 06, pN.PAG
- ISSN
1793-8309
- Publication type
Article
- DOI
10.1142/S1793830920500743