Publicação: Expansivity and shadowing in linear dynamics
Carregando...
Arquivos
Data
Orientador
Coorientador
Pós-graduação
Curso de graduação
Título da Revista
ISSN da Revista
Título de Volume
Editor
Elsevier B.V.
Tipo
Artigo
Direito de acesso
Acesso aberto
Resumo
In the early 1970's Eisenberg and Hedlund investigated relationships between expansivity and spectrum of operators on Banach spaces. In this paper we establish relationships between notions of expansivity and hypercyclicity, supercyclicity, Li-Yorke chaos and shadowing. In the case that the Banach space is c(0) or l(p) (1 <= p < infinity), we give complete characterizations of weighted shifts which satisfy various notions of expansivity. We also establish new relationships between notions of expansivity and spectrum. Moreover, we study various notions of shadowing for operators on Banach spaces. In particular, we solve a basic problem in linear dynamics by proving the existence of nonhyperbolic invertible operators with the shadowing property. This contrasts with the expected results for nonlinear dynamics on compact manifolds, illuminating the richness of dynamics of infinite dimensional linear operators. (C) 2017 Elsevier Inc. All rights reserved.
Descrição
Palavras-chave
Expansive, Hypercyclic, Li-Yorke, Hyperbolic, Shadowing, Weighted shifts
Idioma
Inglês
Como citar
Journal Of Mathematical Analysis And Applications. San Diego: Academic Press Inc Elsevier Science, v. 461, n. 1, p. 796-816, 2018.
