{"title":"Common hypercyclic vectors and dimension of the parameter set","authors":"F. Bayart, Fernando Costa, Q. Menet","doi":"10.1512/iumj.2022.71.9369","DOIUrl":null,"url":null,"abstract":"We investigate the existence of a common hypercyclic vector for a family (Tλ)λ∈Λ of hypercyclic operators acting on the same Banach space X. We give positive and negative results involving the dimension of Λ and the regularity of each map λ ∈ Λ 7→ T λ x, x ∈ X, n ∈ N.","PeriodicalId":50369,"journal":{"name":"Indiana University Mathematics Journal","volume":" ","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2021-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indiana University Mathematics Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1512/iumj.2022.71.9369","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
We investigate the existence of a common hypercyclic vector for a family (Tλ)λ∈Λ of hypercyclic operators acting on the same Banach space X. We give positive and negative results involving the dimension of Λ and the regularity of each map λ ∈ Λ 7→ T λ x, x ∈ X, n ∈ N.
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