Bermúdez, T.; Bonilla, A.; Martínez Jiménez, F.; Peris Manguillot, A. (2011). Li–Yorke and distributionally chaotic operators. Journal of Mathematical Analysis and Applications. 373:83-93. https://doi.org/10.1016/j.jmaa.2010.06.011
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/31441
Title:
|
Li–Yorke and distributionally chaotic operators
|
Author:
|
Bermúdez, T.
Bonilla, A.
Martínez Jiménez, Félix
Peris Manguillot, Alfredo
|
UPV Unit:
|
Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
|
Issued date:
|
|
Abstract:
|
We study Li-Yorke chaos and distributional chaos for operators on Banach spaces. More precisely, we characterize Li-Yorke chaos in terms of the existence of irregular vectors. Sufficient "computable" criteria for distributional ...[+]
We study Li-Yorke chaos and distributional chaos for operators on Banach spaces. More precisely, we characterize Li-Yorke chaos in terms of the existence of irregular vectors. Sufficient "computable" criteria for distributional and Li-Yorke chaos are given, together with the existence of dense scrambled sets under some additional conditions. We also obtain certain spectral properties. Finally, we show that every infinite dimensional separable Banach space admits a distributionally chaotic operator which is also hypercyclic. © 2010 Elsevier Inc.
[-]
|
Subjects:
|
Distributional chaos
,
Distributionally irregular vectors
,
Irregular vector
,
Li-Yorke chaos
,
Weighted shift operators
|
Copyrigths:
|
Reserva de todos los derechos
|
Source:
|
Journal of Mathematical Analysis and Applications. (issn:
0022-247X
)
|
DOI:
|
10.1016/j.jmaa.2010.06.011
|
Publisher:
|
Elsevier
|
Publisher version:
|
http://dx.doi.org/10.1016/j.jmaa.2010.06.011
|
Project ID:
|
info:eu-repo/grantAgreement/MEC//MTM2007-64222/ES/HIPERCICLICIDAD Y CAOS DE OPERADORES/
info:eu-repo/grantAgreement/GVA//PROMETEO08%2F2008%2F101/ES/Análisis funcional, teoría de operadores y aplicaciones/
info:eu-repo/grantAgreement/MICINN//MTM2008-05891/ES/ESPACIOS DE FUNCIONES ANALITICAS, DINAMICA DE OPERADORES Y ESTIMACIONES CON PESOS/
info:eu-repo/grantAgreement/MICINN//MTM2010-14909/ES/HIPERCICLICIDAD Y CAOS DE OPERADORES/
|
Thanks:
|
The second author is supported in part by MEC and FEDER, Project MTM2008-05891. The third and fourth authors are supported in part by MEC and FEDER, Projects MTM2007-64222, MTM2010-14909 and by Generalitat Velenciana. ...[+]
The second author is supported in part by MEC and FEDER, Project MTM2008-05891. The third and fourth authors are supported in part by MEC and FEDER, Projects MTM2007-64222, MTM2010-14909 and by Generalitat Velenciana. Project PROMETEO/2008/101. We want to thank the referee for the suggestions.
[-]
|
Type:
|
Artículo
|