On Intervals, Sensitivity Implies Chaos
In this note we investigate which properties can be derived for a continuous function f defined on an interval I if the only a priori given information is its sensitive dependence on initial conditions. Our main result is the following: If f is sensitive, then f is chaotic, in the sense of Devaney, o...
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2003 |
| País: | Colombia |
| Recursos: | Universidad Industrial de Santander |
| Repositorio: | Repositorio UIS |
| Idioma: | español |
| OAI Identifier: | oai:noesis.uis.edu.co:20.500.14071/7094 |
| Acesso em linha: | https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/530 https://noesis.uis.edu.co/handle/20.500.14071/7094 |
| Access Level: | acceso abierto |
| Palavra-chave: | entire functions chaotic maps |
| Resumo: | In this note we investigate which properties can be derived for a continuous function f defined on an interval I if the only a priori given information is its sensitive dependence on initial conditions. Our main result is the following: If f is sensitive, then f is chaotic, in the sense of Devaney, on a nonempty interior subset of I; the set of aperiodic points is dense in I as well as the set of asintotically periodic points; moreover, f has positive topological entropy. |
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