On Intervals, Sensitivity Implies Chaos

• Autores: Héctor Méndez Lango
• Localización: Integración: Temas de matemáticas, ISSN 0120-419X, Vol. 21, Nº. 1-2, 2003, págs. 15-23
• Idioma: inglés
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• Resumen

  • 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.