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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

hadowing and structural stability for operator

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Author(s):
Bernardes, Jr., Nilson C. [1] ; Messaoudi, Ali [2]
Total Authors: 2
Affiliation:
[1] Univ Fed Rio de Janeiro, Inst Matemat, Dept Matemat Aplicada, Caixa Postal 68530, BR-21945970 Rio De Janeiro, RJ - Brazil
[2] Univ Estadual Paulista, Dept Matemat, Rua Cristovao Colombo 2265, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: Ergodic Theory and Dynamical Systems; v. 41, n. 4, p. 961-980, APR 2021.
Web of Science Citations: 6
Abstract

A well-known result in the area of dynamical systems asserts that any invertible hyperbolic operator on any Banach space is structurally stable. This result was originally obtained by Hartman in 1960 for operators on finite-dimensional spaces. The general case was independently obtained by Palis and Pugh around 1968. We will exhibit a class of examples of structurally stable operators that are not hyperbolic, thereby showing that the converse of the above-mentioned result is false in general. We will also prove that an invertible operator on a Banach space is hyperbolic if and only if it is expansive and has the shadowing property. Moreover, we will show that if a structurally stable operator is expansive, then it must be uniformly expansive. Finally, we will characterize the weighted shifts on the spaces c(0)(Z) and l(p)(Z) (1 <= p < infinity) that satisfy the shadowing property. (AU)

FAPESP's process: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II
Grantee:Claudio Aguinaldo Buzzi
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 17/22588-0 - Dynamics, operators and ergodicity
Grantee:Ali Messaoudi
Support Opportunities: Research Grants - Visiting Researcher Grant - Brazil