{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:39:19Z","timestamp":1740155959537,"version":"3.37.3"},"reference-count":9,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"DOI":"10.13039\/100014718","name":"Innovative Research Group Project of the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11961050"],"award-info":[{"award-number":["11961050"]}],"id":[{"id":"10.13039\/100014718","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2020,12]]},"abstract":"<jats:p> In this paper, we investigate the linear dynamical system [Formula: see text], where [Formula: see text] is the ring of integers modulo [Formula: see text] ([Formula: see text] is a prime). In order to facilitate the visualization of this system, we associate a graph [Formula: see text] on it, whose nodes are the points of [Formula: see text], and for which there is an arrow from [Formula: see text] to [Formula: see text], when [Formula: see text] for a fixed [Formula: see text] matrix [Formula: see text]. In this paper, the in-degree of each node in [Formula: see text] is obtained, and a complete description of [Formula: see text] is given, when [Formula: see text] is an idempotent matrix, or a nilpotent matrix, or a diagonal matrix. The results in this paper generalize Elspas\u2019 [1959] and Toledo\u2019s [2005]. <\/jats:p>","DOI":"10.1142\/s1793830920500743","type":"journal-article","created":{"date-parts":[[2020,6,4]],"date-time":"2020-06-04T03:25:45Z","timestamp":1591241145000},"page":"2050074","source":"Crossref","is-referenced-by-count":0,"title":["Linear dynamical systems of dimension two over the ring of integers modulo pt"],"prefix":"10.1142","volume":"12","author":[{"given":"Yangjiang","family":"Wei","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Nanning Normal University, Nanning 530299, P. R. China"}]},{"given":"Heyan","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Nanning Normal University, Nanning 530299, P. R. China"}]},{"given":"Linhua","family":"Liang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Nanning Normal University, Nanning 530299, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2020,7,25]]},"reference":[{"volume-title":"Matrices over Commutative Rings.","year":"1993","author":"Brown W. C.","key":"S1793830920500743BIB001"},{"issue":"3","key":"S1793830920500743BIB002","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1080\/00029890.1990.11995580","volume":"97","author":"Richter R. B.","year":"1990","journal-title":"Am. Math. Monthly"},{"key":"S1793830920500743BIB003","first-page":"333","volume":"16","author":"Col\u00f3n\u2013Reyes O.","year":"2006","journal-title":"J. Complex Syst."},{"key":"S1793830920500743BIB004","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1016\/j.ejc.2004.06.018","volume":"26","author":"Deng A.","year":"2005","journal-title":"European J. Combin."},{"key":"S1793830920500743BIB005","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1109\/TCT.1959.1086506","volume":"6","author":"Elspas B.","year":"1959","journal-title":"IRE Trans. on Circ. 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