Arithmetic Progressions and Chaos in Linear Dynamics
We characterize chaotic linear operators on reflexive Banach spaces in terms of the existence of long arithmetic progressions in the sets of return times. We also show that this characterization does not hold for arbitrary Banach spaces. To achieve this, we study F-hypercyclicity for a family of sub...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/216752 |
| Acceso en línea: | http://hdl.handle.net/11336/216752 |
| Access Level: | acceso abierto |
| Palabra clave: | ARITHMETIC PROGRESSIONS CHAOTIC OPERATORS FURSTENBERG FAMILIES HYPERCYLIC OPERATORS SMALL PERIODIC SETS https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | We characterize chaotic linear operators on reflexive Banach spaces in terms of the existence of long arithmetic progressions in the sets of return times. We also show that this characterization does not hold for arbitrary Banach spaces. To achieve this, we study F-hypercyclicity for a family of subsets of the natural numbers associated to the existence of arbitrarily long arithmetic progressions. |
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