Artículos de revistas
Expansivity and shadowing in linear dynamics
Fecha
2018-05-01Registro en:
Journal Of Mathematical Analysis And Applications. San Diego: Academic Press Inc Elsevier Science, v. 461, n. 1, p. 796-816, 2018.
0022-247X
10.1016/j.jmaa.2017.11.059
WOS:000426141100044
WOS000426141100044.pdf
Autor
Universidade Federal do Rio de Janeiro (UFRJ)
Universidade Federal de São Paulo (UNIFESP)
Univ Louisville
Ashoka Univ
Universidade Estadual Paulista (Unesp)
Inst Nacl Matemat Pura & Aplicada
Institución
Resumen
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.