Set-Valued Chaos in Linear Dynamics
[EN] We study several notions of chaos for hyperspace dynamics associated to continuous linear operators. More precisely, we consider a continuous linear operator on a topological vector space X, and the natural hyperspace extensions and of T to the spaces of compact subsets of X and of convex compa...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2017 |
| 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:10251/107461 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/107461 |
| Access Level: | acceso abierto |
| Palabra clave: | Hyperspace dynamics Linear dynamics Devaney chaos Li-Yorke chaos Mixing properties MATEMATICA APLICADA |
| Sumario: | [EN] We study several notions of chaos for hyperspace dynamics associated to continuous linear operators. More precisely, we consider a continuous linear operator on a topological vector space X, and the natural hyperspace extensions and of T to the spaces of compact subsets of X and of convex compact subsets of X, respectively, endowed with the Vietoris topology. We show that, when X is a complete locally convex space (respectively, a locally convex space), then Devaney chaos (respectively, topological ergodicity) is equivalent for the maps T, and . Also, under very general conditions, we obtain analogous equivalences for Li-Yorke chaos. Finally, some remarks concerning the topological transitivity and weak mixing properties are included, extending results in Banks (Chaos Solitons Fractals 25(3):681-685, 2005) and Peris (Chaos Solitons Fractals 26(1):19-23, 2005). |
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