Chain recurrence and average shadowing in dynamics

Bibliographic Details
Main Author: Alves, Fabricio F.
Publication Date: 2021
Other Authors: Bernardes, Nilson C., Messaoudi, Ali [UNESP]
Format: Article
Language: eng
Source: Repositório Institucional da UNESP
Download full: http://dx.doi.org/10.1007/s00605-021-01617-6
http://hdl.handle.net/11449/233473
Summary: We investigate several notions related to pseudotrajectories, including chain recurrence and shadowing properties, for a special class of diffeomorphisms on euclidean spheres, known as spherical linear transformations, and for bounded linear operators on Banach spaces. Our main results are complete characterizations of chain recurrence for spherical linear transformations on euclidean spheres and for weighted shifts on the classical Banach sequence spaces c and ℓp. Another main result is a characterization of hyperbolicity for invertible operators on Banach spaces by means of average expansivity and the average shadowing property.
id UNSP_6404eae4727be9f99131a38746a77d9f
oai_identifier_str oai:repositorio.unesp.br:11449/233473
network_acronym_str UNSP
network_name_str Repositório Institucional da UNESP
repository_id_str 2946
spelling Chain recurrence and average shadowing in dynamicsChain recurrenceLinear operatorsPseudotrajectoriesShadowing propertiesSpherical linear transformationsWeighted shiftsWe investigate several notions related to pseudotrajectories, including chain recurrence and shadowing properties, for a special class of diffeomorphisms on euclidean spheres, known as spherical linear transformations, and for bounded linear operators on Banach spaces. Our main results are complete characterizations of chain recurrence for spherical linear transformations on euclidean spheres and for weighted shifts on the classical Banach sequence spaces c and ℓp. Another main result is a characterization of hyperbolicity for invertible operators on Banach spaces by means of average expansivity and the average shadowing property.Instituto Federal de Educação Ciência e Tecnologia de São Paulo Campus Presidente Epitácio, Rua José Ramos Junior, 27-50Departamento de Matemática Aplicada Instituto de Matemática Universidade Federal do Rio de Janeiro, Caixa Postal 68530Departamento de Matemática Universidade Estadual Paulista, Rua Cristóvão Colombo, 2265, Jardim NazarethDepartamento de Matemática Universidade Estadual Paulista, Rua Cristóvão Colombo, 2265, Jardim NazarethCiência e Tecnologia de São PauloUniversidade Federal do Rio de Janeiro (UFRJ)Universidade Estadual Paulista (UNESP)Alves, Fabricio F.Bernardes, Nilson C.Messaoudi, Ali [UNESP]2022-05-01T08:45:02Z2022-05-01T08:45:02Z2021-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1007/s00605-021-01617-6Monatshefte fur Mathematik.0026-9255http://hdl.handle.net/11449/23347310.1007/s00605-021-01617-62-s2.0-85114226669Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengMonatshefte fur Mathematikinfo:eu-repo/semantics/openAccess2024-11-01T14:27:31Zoai:repositorio.unesp.br:11449/233473Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462024-11-01T14:27:31Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Chain recurrence and average shadowing in dynamics
title Chain recurrence and average shadowing in dynamics
spellingShingle Chain recurrence and average shadowing in dynamics
Alves, Fabricio F.
Chain recurrence
Linear operators
Pseudotrajectories
Shadowing properties
Spherical linear transformations
Weighted shifts
title_short Chain recurrence and average shadowing in dynamics
title_full Chain recurrence and average shadowing in dynamics
title_fullStr Chain recurrence and average shadowing in dynamics
title_full_unstemmed Chain recurrence and average shadowing in dynamics
title_sort Chain recurrence and average shadowing in dynamics
author Alves, Fabricio F.
author_facet Alves, Fabricio F.
Bernardes, Nilson C.
Messaoudi, Ali [UNESP]
author_role author
author2 Bernardes, Nilson C.
Messaoudi, Ali [UNESP]
author2_role author
author
dc.contributor.none.fl_str_mv Ciência e Tecnologia de São Paulo
Universidade Federal do Rio de Janeiro (UFRJ)
Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Alves, Fabricio F.
Bernardes, Nilson C.
Messaoudi, Ali [UNESP]
dc.subject.por.fl_str_mv Chain recurrence
Linear operators
Pseudotrajectories
Shadowing properties
Spherical linear transformations
Weighted shifts
topic Chain recurrence
Linear operators
Pseudotrajectories
Shadowing properties
Spherical linear transformations
Weighted shifts
description We investigate several notions related to pseudotrajectories, including chain recurrence and shadowing properties, for a special class of diffeomorphisms on euclidean spheres, known as spherical linear transformations, and for bounded linear operators on Banach spaces. Our main results are complete characterizations of chain recurrence for spherical linear transformations on euclidean spheres and for weighted shifts on the classical Banach sequence spaces c and ℓp. Another main result is a characterization of hyperbolicity for invertible operators on Banach spaces by means of average expansivity and the average shadowing property.
publishDate 2021
dc.date.none.fl_str_mv 2021-01-01
2022-05-01T08:45:02Z
2022-05-01T08:45:02Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1007/s00605-021-01617-6
Monatshefte fur Mathematik.
0026-9255
http://hdl.handle.net/11449/233473
10.1007/s00605-021-01617-6
2-s2.0-85114226669
url http://dx.doi.org/10.1007/s00605-021-01617-6
http://hdl.handle.net/11449/233473
identifier_str_mv Monatshefte fur Mathematik.
0026-9255
10.1007/s00605-021-01617-6
2-s2.0-85114226669
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Monatshefte fur Mathematik
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv repositoriounesp@unesp.br
_version_ 1834483935365562368

Similar Items