On Intervals, Sensitivity Implies Chaos

Revista Integración

关键词: entire functions;    chaotic maps;   

DOI  :  

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown