Distributional chaos for operators on Banach spaces
[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 answ...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/147538 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/147538 |
| Access Level: | acceso abierto |
| Palabra clave: | Distributional chaos Hypercyclicity Upper-frequent hypercyclicity Distributionally irregular vector Absolutely mean irregular vector MATEMATICA APLICADA |
| Sumario: | [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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