Resumen:
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[EN] Four notions of distributional chaos, namely DC1, DC2, DC21/2 and DC3, are studied within the framework of operators on Banach spaces.. It is known that, for general dynamical systems, DC1 subset of DC2 subset of ...[+]
[EN] Four notions of distributional chaos, namely DC1, DC2, DC21/2 and DC3, are studied within the framework of operators on Banach spaces.. It is known that, for general dynamical systems, DC1 subset of DC2 subset of DC21/2 subset of DC3. We show that DC1 and DC2 coincide in our context, which answers a natural question. In contrast, there exist DC21/2 operators which are not DC2. Under the condition that there exists a dense set X-0 subset of X such that T(n)x -> 0 for any x is an element of X-0, DC3 operators are shown to be DC1. Moreover, we prove that any upper-frequently hypercyclic operator is DC21/2. Finally, several examples are provided to distinguish between different notions of distributional chaos, Li-Yorke chaos and irregularity. (C) 2017 Elsevier Inc. All rights reserved.
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Código del Proyecto:
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info:eu-repo/grantAgreement/NSFC//11601449/
...[+]
info:eu-repo/grantAgreement/NSFC//11601449/
info:eu-repo/grantAgreement/SWPU//2015QHZ029/
info:eu-repo/grantAgreement/GVA//PROMETEOII%2F2013%2F013/ES/Análisis funcional, teoría de operadores y sus aplicaciones (AFUNTOP)/
info:eu-repo/grantAgreement/MINECO//MTM2013-47093-P/ES/HIPERCICLICIDAD Y CAOS DE OPERADORES/
info:eu-repo/grantAgreement/MINECO//MTM2016-75963-P/ES/DINAMICA DE OPERADORES/
info:eu-repo/grantAgreement/GVA//PROMETEO%2F2017%2F102/ES/ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y APLICACIONES/
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Agradecimientos:
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This work was partially done on a visit of the first author to the Departament de Matematica Aplicada at Universitat Politecnica de Valencia (Spain), and he is very grateful for the hospitality. The first author was supported ...[+]
This work was partially done on a visit of the first author to the Departament de Matematica Aplicada at Universitat Politecnica de Valencia (Spain), and he is very grateful for the hospitality. The first author was supported by CNPq (Brazil) and by the EBW + Project (Erasmus Mundus Programme). The second and the third authors were supported by MINECO, Projects MTM2013-47093-P and MTM2016-75963-P, and by Generalitat Valenciana, Projects PROMETEOII/2013/013 and PROMETEO/2017/102. The fourth author was supported by the scientific research starting project of Southwest Petroleum University (No. 2015QHZ029) and the National Natural Science Foundation of China (No. 11601449). We thank the referee whose suggestions produced an improvement in the presentation of the paper.
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