科研之友
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摘要
Let (X,d) be a compact metric space and (kappa(X),d(H)) be the space of all non-empty compact subsets of X equipped with the Hausdorff metric d(H). The dynamical system (X,f) induces another dynamical system (kappa(X),(f) over bar), where f:X -> X is a continuous map and (f) over bar : kappa(X) -> kappa(X) is defined by (f) over bar (A) = {f (a) : a is an element of A} for any A is an element of kappa(X). In this paper, we introduce the notion of ergodic sensitivity which is a stronger form of sensitivity, and present some sufficient conditions for a dynamical system (X, f) to be ergodically sensitive. Also, it is shown that (f) over bar is syndetically sensitive (resp. multi-sensitive) if and only if f is syndetically sensitive (resp. multi-sensitive). As applications of our results. several examples are given. In particular, it is shown that if a continuous map of a compact metric space is chaotic in the sense of Devaney, then it is ergodically sensitive. Our results improve and extend some existing ones.
- 出版日期2012-6
- 单位广东海洋大学
