{"title":"八元多项式的根与动力学","authors":"Adam Chapman, S. Vishkautsan","doi":"10.46298/cm.9042","DOIUrl":null,"url":null,"abstract":"This paper is devoted to several new results concerning (standard) octonion\npolynomials. The first is the determination of the roots of all right scalar\nmultiples of octonion polynomials. The roots of left multiples are also\ndiscussed, especially over fields of characteristic not 2. We then turn to\nstudy the dynamics of monic quadratic real octonion polynomials, classifying\nthe fixed points into attracting, repelling and ambivalent, and concluding with\na discussion on the behavior of pseudo-periodic points.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Roots and Dynamics of Octonion Polynomials\",\"authors\":\"Adam Chapman, S. Vishkautsan\",\"doi\":\"10.46298/cm.9042\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper is devoted to several new results concerning (standard) octonion\\npolynomials. The first is the determination of the roots of all right scalar\\nmultiples of octonion polynomials. The roots of left multiples are also\\ndiscussed, especially over fields of characteristic not 2. We then turn to\\nstudy the dynamics of monic quadratic real octonion polynomials, classifying\\nthe fixed points into attracting, repelling and ambivalent, and concluding with\\na discussion on the behavior of pseudo-periodic points.\",\"PeriodicalId\":37836,\"journal\":{\"name\":\"Communications in Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-08-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46298/cm.9042\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/cm.9042","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
This paper is devoted to several new results concerning (standard) octonion
polynomials. The first is the determination of the roots of all right scalar
multiples of octonion polynomials. The roots of left multiples are also
discussed, especially over fields of characteristic not 2. We then turn to
study the dynamics of monic quadratic real octonion polynomials, classifying
the fixed points into attracting, repelling and ambivalent, and concluding with
a discussion on the behavior of pseudo-periodic points.
期刊介绍：
Communications in Mathematics publishes research and survey papers in all areas of pure and applied mathematics. To be acceptable for publication, the paper must be significant, original and correct. High quality review papers of interest to a wide range of scientists in mathematics and its applications are equally welcome.
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