{"title":"Dynamics of Chebyshev endomorphisms on some affine algebraic varieties","authors":"Keisuke Uchimura","doi":"10.1215/21562261-10607402","DOIUrl":null,"url":null,"abstract":"Chebyshev polynomials in one variable are typical chaotic maps on the complex 1-space. Chebyshev endomorphisms f on the complex n-space A are also chaotic. The endomorphisms f induce mappings on the quotient space A/G, where G is the dihedral group of order 2(n+1). Using invariant theory we embed A/G as an affine subvariety X in the complex m-space. Then we have morphisms g on X. We study the chaotic properties of g when n = 2 and 3.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1215/21562261-10607402","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Chebyshev polynomials in one variable are typical chaotic maps on the complex 1-space. Chebyshev endomorphisms f on the complex n-space A are also chaotic. The endomorphisms f induce mappings on the quotient space A/G, where G is the dihedral group of order 2(n+1). Using invariant theory we embed A/G as an affine subvariety X in the complex m-space. Then we have morphisms g on X. We study the chaotic properties of g when n = 2 and 3.